Renting a car in punta cana is easy but very expensive but do very in price. most hotels will have a car rental desk somewhere if not the front desk can always call a car rental place that will come pick you up from your hotel.credit card and drivers license is required. The one thing to remember when driving in dominican republic is that there is lots of bad roads with potholes,huge speed bumps,animals on the road some time and most of all there is road laws but very few and no one follows them they sort of just make there own rules when driving, if you are not use to this type of driving i would suggest you don't rent a car but if you are brave and a good driver this should not bother you and is the best way to expore more places where you can't get with local transit or where taxi's would be to expensive to go.
Rental car tip !!! - Always buy "Full Insurance"
The people in the Dominican Drive like maniacs. Most are cruising around on Mopeds that are in terrible shape. In cars, drivers pass without warning, never use signals, and pay no attention to road signs. If you decide to drive, purchase the extra insurance, b/c you will most assuredly get into an accident (unless of course you are used to driving in Italy or New York) :)
Very satisfied with www.prestigecarrentals.com for our car rental in Punta Cana. They guarntee that they will beat the major brands and they did it! When they thru in a free gps that sealed the deal. With out the GPS we would not have enjoyed our day trips as much as we did. Also we used www.prestige-limousine-service.com for our airport shuttle [Juan-Antonio GREAT JOB]