Normally TWA requires paid reservations for the pool, however they are offering one complimentary session per wedding guest. Reservations can be made once you check in but you have to go up to the pool to make them. The pool is also available free of charge on Saturday morning until 10:45am, no resevations required.
If you wanted to venture out of the hotel on Saturday before the wedding there is public transportation into the city. We highly recommend you leave early and give enough time for any delays etc .... Best way to go would be taking the AirTrain to the "A" train at the Howard Beach JFK airport stop. The A train makes numerous stops throughout Manhattan. The ride is probably an hour or so. Again - please plan wisely. Anyone driving or taking a taxi or car service should definitely be mindful of both beach traffic and crazy airport construction (sorry).
This link has some more suggestions of things to do nearby. Again please be mindful of beach traffic and traffic due to airport construciton and plan accordingly.