Flight
San Juan is a more widely accessible airport however it is about a 2 hour drive from Rincon so you will need to drive quite a bit once you land.
Travel Note
When we visit Rincon we prefer to stay at Vacation rentals. There is a wide selection of them that are really cool and unique to stay in. We suggest you consider this option primarily. Click the link and go to "lodging" for local listings of vacation rentals. Otherwise, Airbnb.com, booking.com, and homeaway.com have a bunch of listings. Be sure to coordinate with each other to share vacation rentals so you can save more money!
House Or Rental
This is an example of an Inn that a large group can stay in. It sleeps 15-20 people and can be very affordable if everyone shares the cost. You can find a bunch more like these on vacation rental websites. Also, we are happy to help anyone coordinate lodging if you need it.
Hotel
We've stayed here, it has a nice pool bar, private beach, and isn't far from the wedding venue but the prices are on the upper end. There are also a wide variety of hotels and this is by no means the only nice place to stay in Rincon. Websites like booking.com and kayak.com can provide a lot of options for you.
Travel Note
American cellphone services work in Puerto Rico and we suggest you utilize google maps for directions to get around. Very few locations in Rincon, PR actually have a street address so having the GPS location in the app helps a lot.