It was during the home inspection on their 1920s colonial in Darien, Conn., that Josh Peschko got the sense that he and his wife, Kristy, had chosen not just the right town, but the right neighborhood.

“School had just let out, and there were kids coming out of every nook and cranny, cutting across our lawn and everyone else’s,” said Mr. Peschko, 36, an asset manager, describing the scene outside their three-bedroom house, which is situated between Holmes Elementary School and Woodland Park. “There are no fences, and we’re right in the middle of it. It’s a shared area, so of course you’ve got to like that kind of thing.”