I get most of my info from allears.net!! This was a question posed to Anita Answer (who has since left allears =( )which I think will help you also? I hope so!!!
"We are taking Disney's Magical Express from the airport to Walt Disney World and then back. Since we are going to be staying at Disney for several days we are thinking about taking a day to go to [the ocean, other theme parks, shopping, etc.]. Is there any place on Disney property to rent a car just for a day? Thanks."
"Hi Everyone!
There are several places to pick up and drop off a rental car on property. The easiest and most convenient is the Alamo/National office at the Disney Car Care Center near the Magic Kingdom. They will pick you up at your resort, and take you back when you return the car. Call 407-824-3470 or visit their websites to reserve. Alamo also has an office at the Dolphin (407-934-4930) as does National (407-825-1876).
In addition, many of the Hotel Plaza Boulevard hotels have rental offices. Keep in mind that these satellite offices have been known to change locations and sometimes close entirely, but here is what was current as of this writing:
Alamo has a third location at the Buena Vista Palace (407-827-2847).
Budget has an office at the DoubleTree (407-827-6089) and has free pick up service.
Dollar is located at the Regal Sun Resort (407-583-8000).
National's third location is at the Buena Vista Palace (407-827-6048).
TIPS: Generally, you can get a better deal by booking via the rental agency websites. Discount codes can often be found on Mousesavers.com. It can also pay off to join the agencies' loyalty programs, which are usually free to join. Members often get the best prices and some programs allow you to skip long lines to boot.
Happy travels, everyone!
A.A."