Tina Naser knew she wanted to live in Manhattan’s West Village, a vibrant neighborhood with historic buildings and distinctive shops and restaurants. But after two years of searching for a one-bedroom apartment, she gave up.

Instead, she opted for a place in a pre-war building within the same neighborhood. Her choice: a 650-square-foot studio apartment, which she purchased in 2012 for $600,000; she spent another $200,000 on renovations, including the kitchen and bathroom. By going with a studio, Ms. Naser, a 42-year-old management...