“Until Aram brought it up, buying an apartment wouldn’t have even entered my mind as a possibility,” Ms. Rubin said. “He went through a million calculations and proved in the long run we would save a lot of money. My whole life, I grew up thinking I would be renting forever in the city. I approached the hunt with trepidation.”

With a budget of up to $400,000 for a co-op, they checked out some places in Kips Bay, convenient to the hospitals on First Avenue in the 20s and 30s. Ms. Rubin liked a late 1950s building on East 33rd Street, where a ground-floor studio had a separate kitchen and a view of a concrete wall.

Image A building on East 33rd Street was an early candidate, but Dr. Modrek had his heart set on the East Village. Credit... Robert Wright for The New York Times

The asking price was $400,000, with maintenance in the mid-$700s, but Dr. Modrek wasn’t keen on the neighborhood. “I had my heart set on the East Village, but it is hard to find a studio in that price range,” he said.

In Tudor City, a bit farther north and east, they saw a tiny, boxy studio with a Murphy bed. The price, below $300,000, was tempting. “I thought we would save a ton of money,” Ms. Rubin said. “But Aram talked some sense into me. It would have been a struggle to live there.”

In the East Village, a one-bedroom on East Second Street was listed for $399,000, with maintenance in the mid-$500s. But it was facing the street, a siren corridor with a firehouse on the next block. That one was tough to turn down, Dr. Modrek said, but “the fire trucks come out sirens blasting,” which was a deal-breaker.