The Great South Bay has been my home cruising territory for 30 years. Do not try to get from GSB to Shinnecock Bay inside. A recent NTM said there shoaling to 1.5 ft. in Moriches Bay. Moriches Inlet is STRICTLY a local knowledge inlet. Duck into Fire Is. inlet and anchor in what is known locally as Sore Thumb (just off the Oak Beach Inn). Then go back out the inlet and down to Shinnecock on the outside. Anchor just off the beach right past the fishing fleet docks. Then back out the inlet and off to Block.
GSB does not have many transiting sailors and there are really only locally known places. You will not find marinas that accomodate boats in transit.
By the way, this assumes you are experienced with running South Shore inlets. Even FI and Shinnecock (which are the best of the lot) can be dangerous to small boats. Transit inlets only on the flood tide (no matter whether you are entering or exiting) unless waves are under 2 ft on the ocean. On the inside of the inlets, there is a lot of shallow water and the channel is constantly shifting. Make sure you have up-to-date charts and follow the Notices to Mariners. All those inlets are notorious.