“One of the great things about Matt is that when he determines there is something beneficial, he gets laser-focused about the process,” Ms. Yasuoka, 27, said. “He started scheduling viewings left and right.”

Apartments came and went quickly. Mr. Cody would send hasty texts to Ms. Yasuoka, who works at a tech company in the East Village, asking if she could rush over for viewings. Along the way, he encountered a revolving door of agents. “I thought it was going to be more of a relationship-type thing,” he said.

The couple checked out one of the area’s few prewar elevator rental buildings, which had a basement gym. The doorman pointed them to several vacancies. A studio on a low floor with little light was going for $3,375 a month, while one on a higher floor, with a bright westward view of the Hudson River and New Jersey, was $3,825.

Image A one-bedroom in a building on Perry Street had its own washer-dryer, but the bedroom was tiny and the balcony was barely there. Credit... Katherine Marks for The New York Times

“I instantly fell in love, but we didn’t exactly love the price,” Ms. Yasuoka said.

At a one-bedroom on Perry Street, with its own washer-dryer, they were excited to hear there was a balcony. But the bedroom was barely large enough for a bed, and most of the Juliet balcony was consumed by the door swing.

Mr. Cody carried a tape measure as they went, and they mapped out their furniture on the computer.

“This one was the most Tetris out of all of them,” he said of the one-bedroom. They were worried that what little furniture they had wouldn’t fit. And the rent was pushing $4,000.

“In these real estate listings, there is a little bit of embellishment involved, and this certainly was one of those cases,” Ms. Yasuoka said. “I wouldn’t call it a balcony. There was a piece of metal that you could sit on.”