Alamo/National also has locations at the Walt Disney World Dolphin and the Hilton Buena Vista Palace. That might be the best location for you depends upon your starting point.
If you will be in a theme park right before needing your car, the Walt Disney World Dolphin location might be best:
The Walt Disney World Dolphin is within walking distance of Epcot (via the International Gateway in the World Showcase) and Disney's Hollywood Studios. You can also get there via boat from Disney's Hollywood Studios. And technically, you can take a Disney bus from any of the theme parks to reach that hotel.
If you will be at Disney Springs, right before needing your car, the Hilton Buena Vista Palace might be best:
The Hilton Buena Vista Palace is located across the street from the Marketplace section of Disney Springs. You can take a bus from your Disney Resort and walk over. This would involve more walking than the shuttle to the Car Care Center, but it might make sense if you're already at Disney Springs.