Alamo/National are at the Swan & Dolphin and the Car Care Center (outside the MK parking lot). The CCC has a shuttle service to get you to/from your hotel.
Other companies have locations at the Downtown Disney hotels.
Make sure you price you rental two or three weeks before your trip because it usually ends up being cheaper to keep your car for the entire trip, rather than dropping it off at a non-airport location. Around 21 to 14 days out from trip, rental rates at the airport often fall dramatically, and you could end up paying more to keep a car for fewer days by not returning it to the airport, even if it sits in the hotel lot going nowhere.
ETA: just did a search using Costco travel, assuming arrival on 9/15 and departing on 9/22. Keeping the car the entire time, renting and returning at the airport, you can get an economy at Budget for $113 (all taxes included) or $136 for a full-size. Picking up at MCO but dropping off at a DTD hotel on 9/18 an economy is $92 and a full size would be $115. personally, I like having the car to get to the water parks and for an additional $21 you can keep it the entire vacation.