SAG HARBOR, N.Y.—This picturesque enclave on the eastern end of Long Island has lately been fretful about happiness.

The cause of distress: a national magazine, Coastal Living, named Sag Harbor as a finalist in a contest to crown "America's happiest seaside town."

Debbie Rudoy, owner of Life'style, an upscale women's boutique on Main Street, was elated. She sees a bonanza in a win for Sag Harbor, with tourists pouring into a village cherished by the likes of John Steinbeck.

"Wouldn't it be wonderful if Sag Harbor would be recognized as this cool indie town that has design and style and great coffee?" she says.

But others are less than buoyant to have the moniker foisted upon them. "Is Sag Harbor a happy place? No, Sag Harbor is not about happy," says Mia Grosjean, president of Save Sag Harbor, a preservationist organization. "Do we really want millions and millions of people here? Maybe Main Street would really like it, but would the residents like it? I am not sure."