You can't pick up or drop off rental cars at any of the DVC or any WDW resorts but if you book through National or Dollar they will send a van to pick you up and take you to get the rental car. They will also bring you back to your WDW resort if you drop off a car. National is located at the Car Care Center by MK and Dollar is located at Courtyard by Marriott at DTD. Either Swan or Dolphin used to also have a rental car pick up/drop off but I read recently that it is no longer available.
I have used National at the Dolphin and Avis is available at the Hilton across the street from the shopping village. National is also available at the Car Care Center and they will send a van for you.