Jon Stein and his wife, Polina, have been known to get so antsy to be outdoors that Mr. Stein and his two young daughters have camped out on the terrace of their Lower East Side apartment on Ludlow Street. “It’s a really nice deck,” Mr. Stein, 39, said.

Six years ago, the couple began auditioning vacation destinations for their family, knowing that someday they wanted to buy a weekend home. They tried staying in Hillsdale, in Columbia County, N.Y., and in various towns on Long Island; they tested nearly every beach town on the Jersey Shore.

Two summers ago, they fell hard for Cold Spring, N.Y., a Putnam County village on the Hudson River, a little over an hour from the city, renting a house near a nature preserve with a river view. Although they didn’t find a house to buy there, the experience inspired them to search in other relatively close areas, as their daughters, Sasha, 4, and Sydney, 3, get carsick on long drives. They looked at towns like Bedford and North Salem, exploring places many have long considered — gasp — the suburbs.

When Ms. Stein, 36, a graphic designer, heard a parent at her daughter’s Manhattan preschool raving about the family’s house on Lake Kitchawan, in sleepy Pound Ridge, a town of roughly 5,000 people that is home to the 4,315-acre Ward Pound Ridge Reservation, they found a house on the same lake soon after. The 5,000-square-foot house, which they are renovating, abuts 16 acres of conservancy land. There are views of the 100-acre lake from most rooms, and there is an indoor pool. They paid less than $1 million.