All the major car rental companies have locations here at the airport. One local company, however, with what I have always found to be reasonable rates is Target. This one, however, is right outside Muñoz Marín Airport.
Since I first wrote this tip several years ago, other rental car companies have opened offices in Puerto Rico. I just used Enterprise Car Rental, which is a well-known company in the United States. Their service was good, with convienient office hours.
The one drawback was when I returned the car, I spent half an hour driving around, trying to find their office. I called the office several times, but had no real luck in getting help that way. The problem was, when approaching from the west, there are three exits from the highway with the same name!!! If you use them, bear in mind that they are well out of the airport, requiring a ten-minute drive, which they provide.
Unfortunately, this is a major concern in the entire metropolitan area. Be cautious when entering or leaving your car for people approaching you, especially if you are pulling into a driveway, or even parking in a lonely spot on the street.
Also, BE AWARE, because of this problem, the police outside of downtown San Juan tolerate drivers going through red lights after 10 P.M till dawn. Just slow down and BE SURE to check for oncoming traffic in all directions!