This may sound kinda 'funny', but I agree with both the 'don't rent a car' and 'rent a car' folks. Honestly, you can get to some really amazing places using public transportation. You can get to more pre-selected, off-the-beaten-path type places with a car.

With regard to car rental... All you need is the AAA int'l driver's license, available at any AAA office, and a credit card. If you rent a car GET ONE WITH A NAVIGATION SYSTEM. It is ridiculously easy to get hopelessly lost here. Many (most) streets here do not have names and even natives get confused by road signs.

You won't go wrong either way. I've found some wonderful places by just getting on the train and haphazardly choosing a stop.

Have fun!