Daniel Richards and Michael Wehner loved their little cottage in Sag Harbor, N.Y., which they bought in 2014 as a weekend escape from their primary home in Manhattan. “It’s that classic 1800s whaler’s cottage,” said Mr. Richards, 52, a landscape architect originally from Australia who runs the New York-based firm Daniel Richards Design. The 1,700-square-foot house, which cost them $907,000, was drafty and full of quirks, but that just added to beachy appeal of the place.