I'd just do a search on one of the travel booking sites for Isla Verde/Carolina, or hotels close to the airport. You'll get prices and user reviews for all of your options. Depending on your date there could be a bunch of nice hotels for cheap, or they could be mostly booked with slim pickings left over. If available and within your price range, I would recommend a hotel on the beach. We often stay at the El San Juan for a decent price, but the El can be loud on weekends.

As far as things to do, Isla Verde has the best beach in the San Juan area. With your limited time, I would probably limit activities to the hotel pool and beach. Maybe lunch at the hotel or a nearby restaurant (Metropol is delicious).

BTW, is this time between flights or are you coming from a cruise and catching a flight the next day? Or something else?

Matt