I would try Flynn's in Ocean Bay Park. It's about a 20 minute walk, and they are pretty accommodating. We stay there several weekends each summer. The docking fees include meal credits. Unfortunately, the food is just fair, but you can also use the credits on drinks and t-shirts/hats, etc.
Flynns phone number is 631-583-5000. You can use the pool at the Fire Island Hotel about a block away while you are there. There is also a liquor store and a deli right there.
You can also try Seaview Marina, which is in the town between Ocean Beach and Ocean Bay Park (Seaview). However, they are really nasty, and I'm not sure if they allow transients at all any more, since the town took it over. Good luck.