When the friend who had been living in their Mission District apartment decided to move to New York too, the couple asked if he would be interested in joining them, assuming they found a big enough two-bedroom. He was.

“We figured you could get more space with a two-bedroom, and it would be nice to live with a social friend during our first year,” Mr. Vengrin, 31, said.

The trio were willing to spend into the $7,000s. Mr. Brown showed them a cross-section of apartments in various neighborhoods. One, in a glassy tower with great views, felt uncomfortably small for the price. Another was undergoing renovation, with missing finishes and appliances. “You can’t tell where they will cut corners,” Ms. Sinclair said.

Image In Little Italy, a lovely two-bedroom spread out over an entire floor was priced right. But the stairs were a deal-breaker for the dog. Credit... Katherine Marks for The New York Times

In Little Italy, a pristine and lovely two-bedroom floor-through in a charming three-story brick townhouse was listed for $6,500. But the stairs were a deal-breaker for Pacman.

A spacious two-bedroom on a high floor in a white-brick postwar building near Union Square was available for $7,250. But like many older buildings, it had no amenities to speak of.

On East 14th Street, past Avenue A, the couple visited EVGB. (The acronym stands for “East Village’s Greatest Building” and is a nod to the storied rock club CBGB.) The building, which recently opened on the site of a low-rise commercial strip, advertises a “boutique industrial aesthetic.”