I used to live in Orient (the end of the other fork on Long Island). The end of the island was incredibly lucky and weathered Sandy very well. Here are some things:
I think you mentioned in another post you've been out there before- so you know about the traffic since it is really only a single road and everyone loves visiting there.
-You can go to the end (pretty) and pay the cheap fee to go up the lighthouse.
-Any beach is a great beach.
-Plenty of shopping in South Hampton and East Hampton if you are into that (nice area too).
-If you don't mind a little above average price- Gossmans is the best restaurant. Go for lunch for no line, beautiful view of/on the docks, and slightly cheaper fare.
-I think it is South Hampton that has a Royal Enfield store. They aren't my cup of tea, but look great. You can actually test ride them there!
-Explore. Once you get near Montauk every side road gives you great views and may even be a tiny bit twisty (something Long Island isn't known for).
Hope this helps!