I mentioned on another thread that I wished I could help, but Montauk is a couple hours east of me, and I've never been there. I doubt anyone here lives around there, but most likely someone has been on vacation.
You may not realize how big Long Island is. You'll be 130 miles from NYC. I'd focus more on seafood.
Edit: not sure if this is your first time in the area and you are looking to experience "authentic" ny pizza, bit if that's the case your best bet would be to schedule a stop either leaving or going to the airport. If interested let us know which airport (jfk and la guardia are both in Queens) and someone can probably point you in the right direction.