three mile harbor is nice, we've stayed at east hampton point (www.easthamptonpoint.com), it's a nice palce with a pool and tennis and a upscale restaurant. When I last stayed there a few yesrs ago they had a van that ran to town and the beach during the day (9-5?). I would call to see if this is still offered.
Nothing on three mile harbor is near town. I assume by beach you mean ocean, also not near the harbor. If you want to swim in the harbor or bay I'm sure there is a spot near by.
As others have said if you go through the peconics and the canal you'll be near the ocean and have other options, but it's a little bit of a ride.
If you have not stayed at montauk, I would recommend the montauk Yacht club, it has great facilites (pools indoor and outdoor, tennis, play ground, multiple restaurants, gym, a small beach on the harbor). they have a van to and from town, the ocean beach and the harbor area by Gossmans and it runs, I think, till 9pm and later on weekends. Other places to consider in the peconics, none with an ocean beach, are shelter Island, Sag Harbor(south fork) and Green port(north fork)
Good luck with your planning.
