Still, that amount, they figured, would go a lot further in a neighborhood that didn’t have Gucci and Burberry stores, recent arrivals courtesy of the Brookfield Place renovation. Even their bodega had been replaced by Le Pain Quotidien.

$3,300 | Inwood, Manhattan

Rick and Dana Trader, 48 and 43

Occupation: Ms. Trader is the vice president of employee experience at Meetup; Mr. Trader is in sales at Braze, a mobile marketing company.

Their children: Chloe and Jonathan Wolma, 17 and 15, and Jackson and Wesley Trader, 14 and 12

School commutes: Chloe and Wesley head to the Upper East Side to attend Eleanor Roosevelt High School, where she is a senior, and Robert F. Wagner Middle School, where he is an eighth grader. Jackson is a sophomore at the Bronx High School of Science, which is significantly closer than it was when he was living in Battery Park City. But Jonathan, a sophomore at Millennium High School, now has an hour commute rather than a 10-minute walk.

Why they didn’t stay in Battery Park City: Because of the growing crowds and the cost. After leaving their $4,500-a-month apartment, Ms. Trader said it was re-listed for $2,000 more a month. All the three-bedrooms they saw in the neighborhood cost at least $7,500 month.

Buying in the city: The Traders considered it, but even million-dollar listings would have been a downgrade from their Battery Park City apartment. Instead, they sunk their down payment into an 1890s farmhouse in Salt Point, N.Y., where there is a swimming pool, a barn with a Ping-Pong table and “lots of quiet and space,” Mr. Trader said. “It’s all the things the city is not. We go up there most weekends.”

But Manhattan is not a place with an abundance of reasonably priced family-size apartments.

“Once you go up to something in a family-size range, stuff skyrockets,” Ms. Trader said. “A three-bed is, like, twice the cost of a two-bed.”

And cramped though it felt, they soon learned that their two-bedroom was actually spacious by the standards of the borough.