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.