Westlake Chowder house on Westlake drive is a good local bar with very solid food, sushi etc and an authentic "Montauk" type experience ( not Hamptons). If you want more of a fancy (by Montauk standards) date type experience, try Dave's Grill - fantastic food. Not stuffy or Hamptons like either. You need to make reservations same day and you will need them. Fishing is fantastic now, so go ahead and book a half day trip on one of the Charter boats or party boats... June is great striped bass fishing in Montauk - then Wok and Roll (Chinese Restaurant) will cook it for you! Harvest is also a great restaurant.
John's pancakes on MTK highway has better pancakes than the one across the street. Gaviolas Market, by Gossmans has the best breakfast egg sandwiches. I've never done it, but I always threaten to take my wife horseback riding -
As far as "clubs" I would just barhop in the village one night, and up by the docks the next night. That way, you can just walk or cab it back.