If you're a parent, or plan to become one, the National Association of Realtors knows what's probably on your house-hunting wish list: More than half of home buyers surveyed by the Washington, D.C.-based trade organization sought a property sized to suit a growing family and an even greater number said a convenient neighborhood with nearby places to walk, dine and play was their top priority.

And, of course, parents want their kids to have access to high-quality schools -- a factor that becomes increasingly important as buyers' children reach school age, the research shows.

In the 2013-14 school year, New York State overall had a graduation rate of 76.4 percent. Statewide, 31 percent of graduates earned a Regents diploma with advanced designation -- an achievement that educators regard as an indicator of college readiness because of the rigorous coursework and additional exams required.

Here we highlight Long Island communities with the perks parents want, in school districts where the percentage of graduates earning advanced Regent diplomas exceeded that statewide rate, along with a sampling of what you can get for each county's median sale price -- $470,000 in Nassau and $347,500 in Suffolk in August, according to the Multiple Listing Service of Long Island.

IF YOU WANT A STROLLER-FRIENDLY NEIGHBORHOOD

Try: Huntington

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School stats: In 2014, 43 percent of Huntington High School graduates earned a Regents diploma with advanced designation.

Why you should live here: Some 84 percent of home buyers said having sidewalks and places to walk were important in a 2015 National Association of Realtors community preference survey, and 56 percent said having nearby bike lanes and paths were important to them, too. Huntington homeowners enjoy all of the above.

Parents seeking a baby-friendly fitness challenge won't have far to look -- they can work up a sweat pushing their strollers through Heckscher Park. There are even organized group stroller workouts at the 18-acre town park, such as Stroller Strides. The park has an outstanding playground, too.

Families with tots also love the convenience of strolling the sidewalks for shopping and dining downtown. A favorite stop is the children's section of indie bookstore Book Revue, which has a wooden fire truck for little ones to climb in, as well as a Toddler Time program with music, stories and crafts. Home prices range from $198,000 for a three-bedroom ranch to $3.335 million for a five-bedroom waterfront villa.

Also try: Stony Brook Village is another charming North Shore spot where families with babies in strollers can browse boutiques and enjoy events such as an annual Lego-building contest. Nearby, even a non-sporty stroller can handle a leisurely walk in the woods, thanks to a boardwalk into tranquil Avalon Park.

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Home prices in Stony Brook ranged from $186,000 to $1.699 million in a recent search. Most homes on the market were in the Three Village school district.

On the South Shore, errand day is a pleasure in the village of Massapequa Park, where you can park your car just once, strap your child into the stroller and accomplish your entire to-do list on foot. The paved path through nearby Massapequa Preserve is a stroller-friendly place to enjoy nature.

In a recent search, home prices in Massapequa Park ranged from $332,000 to $925,000. Most homes on the market were in the Massapequa school district.

IF YOU'RE LOOKING FOR ROOM TO GROW

Try: Wantagh

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School facts: In a recent search, more than half of Wantagh homes for sale were in the Wantagh school district, where 64 percent of graduates earned a Regents diploma with advanced designation in 2014. Some homes were in the Levittown school district, where the rate was 60 percent, or Seaford, where the rate was 59 percent.

Why you should live here: Little feet need room to pitter-patter, so it's no surprise that the demand for extra bedrooms remains high. U.S. Census Bureau data in 2014 shows the national percentage of new homes completed with four or more bedrooms has increased for the fifth straight year, to 46 percent, exceeding the percentage of both two- and three-bedroom homes.

Dozens of listed Wantagh homes in a variety of price ranges can accommodate larger broods needing four or more bedrooms. A recent search showed that more than two dozen four-bedroom homes were listed in Nassau County's median price range. Prices for a single-family home here ranged from $325,000 to $1.749 million.

Karen Mazzola of Realty Connect USA, who has listed a five-bedroom home in the community for $479,000, calls Wantagh "an ideal place to live and raise a family," citing its sense of community, easy commute to Manhattan and sought-after schools.

Wantagh residents also enjoy proximity to a number of family-friendly public gems: Nassau County's Wantagh Park offers paths, pools, sports courts and playgrounds for fitness and recreation. Twin Lakes Preserve is a great place for fishing or a family hike.

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And Jones Beach State Park is just a 10-minute drive or five-mile scenic bike ride away.

Also try: If you want more house for the money in Suffolk County, try Holbrook. In a recent search, there were 49 houses for sale with four or more bedrooms, and 17 were in Suffolk's median price range. Yards are big here, too: There were 60 lots larger than 80 by 100 feet, and 36 were listed in the median price range. Home prices in Holbrook ranged from $99,000 for a mobile home to $649,900 for a four-bedroom Colonial. Residents attend Sachem schools.

IF YOU'RE LOOKING FOR OLD-FASHIONED FAMILY FUN

Try: Port Jefferson

School facts: Most homes on the market were in the Port Jefferson school district, where 61 percent of graduates earned a Regents diploma with advanced designation in 2014. Some homes were in the Comsewogue school district, where the rate was 40 percent.

Why you should live here: Comforting hints of yesteryear are woven seamlessly into the busy lives of modern kids in Port Jefferson. Youngsters can explore science and engineering concepts both antiquated and cutting-edge at the Maritime Explorium, a nautical-themed space for kids.

Families can see the latest children's plays in a historic theater building on Main Street. And the classic ending to any family outing is an ice cream cone and walk down by the harbor.

Even as today's families hustle from soccer practice to dance class, the daily rhythm of the village is marked by the sound of a ferry horn, as it has been for generations. The Bridgeport & Port Jefferson Steamboat Co., with service to Bridgeport, Connecticut, has been in operation since 1883.

The village holds an elaborate Dickens festival every winter featuring carriage and trolley rides, characters in period dress, Victorian food and entertainment, storytelling and caroling. Families can complete the idyllic winter experience by skating at the outdoor ice rink against the backdrop of Port Jefferson Harbor. Homes on the market in Port Jefferson range in price from $315,000 to $1.499 million.

Also try: Out east, Greenport's historic buildings, cute shops and a 4-acre waterfront park with a restored antique carousel create a timeless charm that makes this seaport village a family favorite. Prices here range from $295,000 to $1.995 million; however family-sized homes -- those with three or more bedrooms -- start at $399,000. Residents attend Greenport school district.

Families with small-town sensibilities love postcard-pretty Cold Spring Harbor, which has a quaint Main Street historic district. Local kids can travel back in time to their hometown's whaling era days at the Whaling Museum. If you want to live here, it'll cost you: In a recent search of Multiple Listing Service of Long Island, there were no homes available in Nassau's median price range. The lowest price was $599,000. Most homes are in the Cold Spring Harbor school district.

IF YOU'RE LOOKING FOR A BIG BACKYARD

Try: Centereach

School facts: Most homes on the market were in the Middle Country school district, where 40 percent of graduates earned a Regents diploma with advanced designation in 2014.

Why you should live here: More than half of home buyers surveyed prefer a detached home with a sizable yard, according to the National Association of Realtors. In a recent search, 96 Centereach homes had lots of 80 by 100 feet or larger, and 72 of them were listed in the county's median price range. Prices here were moderate, ranging from $159,000 for a two-bedroom ranch on an 80-by-100-foot lot to $599,990 for a four-bedroom Victorian on a half acre.

Cyndi Sheppard of Realty Connect USA says residents enjoy some exceptional public perks.

The Middle Country Library, which has a branch in Centereach, offers children and family services that are so highly regarded that the library was chosen as the national model for the Family Place Libraries, which helps libraries become community hubs for parents and children to gather, develop and learn. Local parks are another plus. "The township of Brookhaven has many recreational activities, like the Centereach pool with water slide, and the community center," Sheppard says.

Also try: Ronkonkoma is another good pick if you want more yard for the money. More than half the homes on the market have lots of 80 by 100 feet or larger, and 56 of them are in the county's median price range. Prices range from $125,000 to $575,000. Most homes on the market were in the Connetquot school district; some were in the Sachem or Middle Country school districts.

In a recent search, only 18 percent of Nassau homes in the median price range had a minimum lot size of 8,000 square feet -- about 0.18 acres. East Meadow's tree-lined residential blocks include numerous homes with lots greater than 80 by 100 feet. There were 21 properties of that size for sale, and about half of them were listed in the county's median price range. Home prices in East Meadow ranged from $280,000 to $879,000. Prices for properties of that size start at $379,000. Most homes are in the East Meadow school district.

IF YOU WANT GREAT PLACES TO PLAY

Try: Bayville

School facts: Most homes on the market were in the Locust Valley school district, where 78 percent of graduates earned a Regents diploma with advanced designation.

Why you should live here: Any way you want to play, the quaint coastal village of Bayville has you covered, with organized sports and activities, beaches, playgrounds and an amusement park and arcade. "Bayville today is the same Bayville of my childhood -- wonderful people, beautiful clean water and beaches," says Patricia Farnell of Douglas Elliman Real Estate.

Ransom Beach seems tailor-made for families with young children. It's small and manageable, it has a fun playground and the water is calm enough for dipping little toes. Across the street is the Bayville Adventure Park, which offers miniature golf, a ropes course, bumper boats, rock climbing and a bungee bounce. An indoor arcade and an ice cream parlor offer fun in any weather. In the fall, there are Halloween-themed activities for kids. Home prices range from $315,000 for a two-bedroom ranch to $3.199 for a four-bedroom waterfront Colonial.

Also try: You won't find a family-sized home in Great Neck for the county's median price range -- in a recent search, the lowest price for a single-family home with three bedrooms was $589,000 -- but if you've got the means, this community offers an exceptional selection of places to play. The Great Neck Park District's 21 parks offer an impressive array of children's amenities such as playgrounds, swimming and sports facilities and programs especially for kids such as outdoor movies, scavenger hunts and sing-alongs. Most homes on the market were in the Great Neck school district.

A more moderately priced neighborhood with great places to play is Hicksville. The community is home to Cantiague Park, a 127-acre Nassau County park with a miniature golf course, a pool and sports facilities and an ice-skating rink -- as well as two Town of Oyster Bay parks with athletic fields and playgrounds. For indoor play, the Hicksville Athletic Center has a wide selection of activities for kids, and in the commercial district, the Broadway Mall hosts Family Fun Days. The mall also has two soft play areas, coin-operated rides and a multiplex theater.

Home prices here range from $289,990 to $799,000. Most homes on the market were in the Hicksville school district; some were in the Bethpage district.

SCHOOL STANDOUTS

Five Long Island high schools made the top 200 in U.S. News & World Report's 2015 list of the country's best high schools: Garden City, Jericho, Great Neck South, Manhasset and Syosset.

There were 733 single-family homes with at least two bedrooms for sale as of press time in those five schools' districts, according to the Multiple Listing Service of Long Island. A search revealed that homes on the market ranged from a three-bedroom, 3 1/2-bath 1740 home being sold as is in Syosset for $379,000 to an 18-room historic French chateau in Brookville for $16.5 million.