You should be able to make it to Montauk and back on one charge, and if not there's Southampton. Future locations in Shirley and Manorville will help you out.Tesla gotta put a supercharger V3 in the Smithtown location. When COVID is over the rush at Islandia supercharger will be as busy as pre Covid and will be inefficient for Tesla owners not to have one in Smithtown.
Tesla doesn't usually offer Public charging at their Service Centers. Syosset no longer has Superchargers. The Destination Chargers at Smithtown are for cars in service, not owners.I would be very disappointed if they don't install a V3 SC suite at Smithtown. Just some L2 chargers there currently. Not like they don't have plenty of room for SC's at that location.
There is a v3 in Copiague, and v2 in Islandia and Plainview. That being said, Superchargers are for trips or if you honestly can't charge at home.