There are a few choices for getting to Rincon.  Fly into San Juan and then either rent a car, use a car service (there are some in Rincon who will pick you up in San Juan) or take a puddle jumper to the west coast of the island.  If you don't hit a lot of traffic, it takes about 2.5 hours from SJU to Rincon.

There is a smaller airport in Aguadilla (BQN) which is about 35 minutes from Rincon.  Jet Blue and United have flights through JFK.  JetBlue also has flights connecting in Orlando.

Spirit Air has flights through Ft. Lauderdale to Aguadilla.