There's actually quite a lot to do around Montauk. There's a lot of fishing I know, although I've never been out fishing. They claim to have more saltwater fishing records than any other port in the world, so it can't be too bad!
And there are a lot of State Parks and Montauk resorts and things like that. I know the oldest operating ranch in the States is there as well but I'm not sure if that's open for visitors or not.