Another option arose in the West 90s. Mr. Leigh emerged from the 96th Street subway to find an appealing neighborhood not far from Riverside Park. This apartment was bigger and better than the others, with two sizable bedrooms and an extension off the living room that nearly qualified as a separate kitchen. There was even a dishwasher.

“He liked the fact that his daughter had a door to her own room,” said Zachary Scott, a colleague of Ms. Aras’s who accompanied Mr. Leigh to the apartment. The rent was $3,100.

By this time, Mr. Leigh had figured out that many buildings in the city — including this one — don’t have a laundry room. “It is hard for me to understand that a city like New York doesn’t have laundry in the apartment,” he said. “On my day off, I don’t want to spend three hours on my laundry. Leisa explained how that works. You can drop off your laundry, and the next day you can pick it up.”

When he returned to show his sister and Ya-Amie, he said, “My daughter went into the bedroom and said, ‘Wow! Papa, this is my room. I like it.’”

Ms. Aras then worked diligently to get Mr. Leigh approved as a renter.

“Here, they have what you call credit history, which in my case is zero,” Mr. Leigh said. “I never lived here. I couldn’t imagine without a professional how to find an apartment here.”