You can’t miss the Second House Museum as you enter downtown Montauk. The building, which dates back to 1797, is the oldest building still standing in Montauk. The house is set up as it was when it was built and offers families a look back in time. Tours are free, with donations welcome. Events such as craft fairs are often hosted here. Open seasonally, Sunday through Tuesday and Thursday through Saturday from 10 a.m. to 4 p.m.; closed Wednesday.