There are supposedly six places to get Mr. Potato Head parts:
1. Once Upon a Toy (Downtown Disney)
2. County Bounty (Toontown Faire at Magic Kingdom)
3. MouseGear (Epcot)
4. L.A. Props (Disney Studios)
5. Chester & Hester Dinosaur Treasures (Animal Kingdom)
6. Everything Pop (Pop Century)
I got parts at MouseGear, L.A. Props, and County Bounty.
You do not have to buy the body at WDW and as it's been mentioned, it's much cheaper to buy a body at a local store. You then can fill the entire box with parts. I managed to cram in a lot of parts; it was kind of like a puzzle.
One thing that I noticed was that the Disney hands are not the same as the hands that come with some of the Mr Potato Heads. Just make sure your Potato has hands that can hold things (clenched fist with round opening).
Each of the store had some of the same things and some different things. If there is something you are specifically looking for you should check the different stores. If you're not fussy, then most of the stores sell the same basics (at least MK, Epcot, and DS, did).