After seven years in their big one-bedroom in the Washington Heights section of Manhattan, Alliana Semjen and Matthew Schwartz were eager to move farther downtown.

The rental, in the Audubon Park Historic District, cost around $2,300 a month. It was in a great location for their bicycling trips to New Jersey, conveniently near the George Washington Bridge. But they were unhappy with the kitchen, which always looked dirty and lacked a hood vent. “We smoked out our apartment so many times,” Mr. Schwartz said.

Out front, they faced nonstop construction. The neighborhood had few restaurants, and when they walked Beacon the dog, they worried he would step on something sharp. “It felt like we were not living in the city, but not living in the suburbs,” Ms. Semjen said, lacking the benefits of both.

So the couple, who met as students at Binghamton University, decided to move to the Upper West Side, which was still convenient to their cycling routes and close to Ms. Semjen’s parents. For up to $1.5 million, they hoped to find a co-op with a good kitchen and three bedrooms (allowing space for a future family), or at least two bedrooms and an office.

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The Upper West Side location would cut their subway commutes to Midtown in half.

Ms. Semjen, 32, does graphic design for a media company. Mr. Schwartz, 34, is a lawyer. And when the two work from home, their styles clash: She sits on the sofa with the TV on in the background; he needs a desk and a room with a door, where he can be free from distractions.

“The setup wasn’t great for our productivity,” Ms. Semjen said. So a suitable work space was essential.

They also preferred a prewar building. “They were willing to do work,” said their real estate agent, Tami Shaoul, of the Corcoran Group. Even so, there was little inventory.

Among their options:

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