There are many right at the airport. Hertz. Avis. National. Eurocar. And several others.
Lindsey
Lindsey is spot on, you can book on-line and have the car waiting for you when you land!
Been there done that a few times. Tried to return a car to the STI airport from POP and sort of got lost. Tried asking for directions and almost got scammed with the escort. Luckily that didn't turn into a disaster. It all worked out in the end but was very stressful trying to find STI. Someday I'll take a trial run late at night when the traffic dies down. I know the people are all trying to make a buck but sometimes it wears you down. Thanks I'll check with the credit card company to see my options are.I have booked on line through expedia. I have found Europcar to have the best prices for compact or economy cars. The agent at POP airport told me that my best option is to book through expedia for the lowest price and convenience. Another thing to consider is that some credit card companies,(master card platinum for example) cover your collision waver and any other damage if you use there card for the rental. What they do not cover is personal injury. So you can save quite a bundle if you book on line using a credit card that will cover collision insurance. I have done this at POP, Santiago airport and La Romana airport.
Renting the car is the easy part, driving here is a whole other forum unto its self.
Good luck.