The Edgemont Community Council, an umbrella organization that dates to 1947 in its current incarnation, represents no fewer than eight neighborhood associations.

About a third of housing is in the form of co-ops, condos and rental units, most along Central Park Avenue, Mr. Sherwin said. These provide the cheapest entry points for the school district and contribute to a degree of economic diversity, especially compared with other parts of Westchester. According to 2014 housing data, 26.4 percent of the homes in Edgemont were valued under $500,000. In Chappaqua, 15 miles north, that figure was 13.4 percent; in Scarsdale village, it was 4.4 percent.

Image 3 ROXBURY ROAD | A six-bedroom, four-and-a-half-bath colonial in Old Edgemont, built in 1920 on 0.42 acres, listed for $1.65 million. 917-836-2717 Credit... Tony Cenicola/The New York Times

Businesses along Central Park Avenue include megabrands like Walgreens, Buy Buy Baby and Red Lobster, as well as small operations like Candlelight Inn, a popular purveyor of pizza and chicken wings. About half of Edgemont’s homes are within walking distance of Scarsdale’s well-stocked commercial district. Hartsdale, to the north, also has shops and restaurants near its train station.

Green spaces thread through the hilly region. Some Edgemont houses back onto golf-course fairways. The middle school and high school occupy a leafy enclave. The Greenburgh Nature Center is a preserve set on 33 acres with trails, live animal exhibits and an array of school programs.

Last month, the Sprain Ridge pool complex reopened in Yonkers, near Edgemont’s southern border, after an extensive renovation funded by the county. It includes a 50-meter-long competition pool that can accommodate 500 swimmers, plus an activity pool and spray deck for children.

What You’ll Pay

At about 3.2 percent, Edgemont’s property taxes are high, even for Westchester. “You’re looking at $30,000 on a million-dollar house, Ms. Weiss said, adding that Scarsdale’s taxes are closer to 2.3 percent. (She noted that these percentages are not consistent across the board: “It’s always house by house and you might get lucky and find a house a bit under-assessed.”)