Since the late 19th century, when the Long Island Rail Road pushed its way out to East Hampton, this has been a destination for the wealthy set of Manhattan. The cultural institutions reflect this history, so in addition to the outright splendor of the beaches, there’s plenty to do on a rainy day. The colonial remnants like the village’s architecture, Hook windmill, and the old cemeteries connect visitors to another time, while the high-end dining and abundance of art galleries keep us at the cutting edge of what’s happening now.