As previously mentioned, there's a hotel inside the airport terminal - basic accommodations.
Embassy Suites is just a few minutes taxi ride from the airport - - it's the closest "off airport" hotel and only a 2 1/2 block walk to a very nice beach.
Other hotels within a 8 to 12 minute taxi ride from the airport are (listed in no particular order):
The Courtyard by Marriott The Ritz-Carlton Fairmont El San Juan Hampton Inn & Suites Royal Sonesta San Juan San Juan Water & Beach Club Hotel
Check out their respective websites then select the one that best fits your budget and "hotel" travel style.