They also wanted to avoid full-service buildings. Mr. Reefer’s two dads live in a Yorkville co-op, “with porters, doormen, gardeners and paint guys, and there is so much tipping and all those rules,” he said. “I am in my 20s. I can carry things upstairs. I wanted an old-school, tenement-style, no-elevator, no-nothing walk-up.”

They emailed about a listing in a beautiful Gramercy Park building, circa 1928, that they found on StreetEasy, and heard from Karen Kostiw, a licensed saleswoman at Warburg Realty. The price was $795,000 when they saw it, having dropped from $975,000. Maintenance was around $1,250 a month. The master bedroom was less than 100 square feet, and the Pullman kitchen was advertised as “smart, sleek and the perfect size for the city dweller.” That meant a dorm-size refrigerator and minimal counter space.

Image A two-bedroom in a 1928 Gramercy Park building was the right price, but it had a kitchen with a dorm-size refrigerator and minimal counter space. Credit... Katherine Marks for The New York Times

“It was less of a kitchen than in most hotels I’ve stayed in,” Mr. Reefer said. “I think that apartment is for a pied-à-terre or for the kind of person, like my friends, who don’t cook but just order out.” The apartment later sold for $750,000.

In Greenwich Village, a two-bedroom in a charming walk-up was going for around $700,000, with maintenance of $1,000. It seemed “incredible for the price, and there was probably a reason for that,” Mrs. Reefer said. “We were blinded by the address and the cool neighborhood.”

As it turned out, a single investor owned most of the co-op shares in the building and was renting many of the units, making a mortgage difficult to obtain.

“The fantasy was we would find something really cheap by being smarter than everybody else, but it was never that realistic,” Mr. Reefer said. Still, they had fun frequenting open houses, lining up an itinerary for the day and stopping for brunch.