Block Island is "okay", IMO, but not the great place everyone makes it out to be. If you want excitement, drunken obnoxious boaters that could give two chits about your boat after having a few, stay at Champlins. If you want less excitement and a moderate experience, stay at the Boat Basin. If you want peace and quiet and relaxation, anchor or get a mooring. With 4 non drinkers along for the trip, I am not sure that BI is the place for you as in recent years it has gone the way of a revitalized frat/sorority house.
I have not been to Montauk in a while, but based on your group, it would be my preferred choice over BI.
Depending on your timing and schedule, another choice is to go the ~15 miles beyond Block Island and make a trip to Newport.