Danielle Caputo, 37, grew up in Bath Beach, Brooklyn, not far from the Verrazano-Narrows Bridge, but had never spent much time on the other side of it, in Staten Island.

Then, in 2015, on the way to visit the Staten Island Zoo, she was impressed by the island’s North Shore, including the walkable, architecturally interesting neighborhood of Stapleton, with its spacious houses; at the time she and her family were renting a two-bedroom apartment in Dyker Heights, Brooklyn.

“I always thought Staten Island was so suburban,” said Ms. Caputo, a hair stylist. “I didn’t think it could be so old and historic.”

A home search ensued, and Ms. Caputo found a nine-bedroom Victorian with views across New York Bay to One World Trade Center. Last fall, it cost $785,000.