Buying a used car is a good idea but do you want to be stuck with the task of selling it back?
If you're going to be driving a fair bit and have the money you should probably get a certified used car, in case you are planning on driving a bit you don't want to chance having to repair the car, which can be very costly. Don't forget most states levy a property tax on cars, so that would be extra expense on top of registration, inspection etc.
If you can avoid buying/selling you probably should. Have you tried some of the "budget" type rentals that rent out used cars maybe they will be more flexible.