I, too, am a coffee snob, so much so that I usually bring a grinder and my own beans when I travel to WDW. However, I have run across a couple of places with pretty good coffee there.
- Kona has press pot coffee. There is a thread somewhere that talks about press pot coffee locations, and in my experience, the coffee they use for those is of quite good quality. I mention Kona 'cause I was there last October. AP used to have the French press, too, but stopped at one point. I'm now hearing they have it again. When they had it a few years ago, it was excellent.
- If you can get into Shades of Green, there actually is a Starbucks kiosk in the main hotel/lobby area (head down toward their ticket and shopping area). I realize views regarding Starbucks run from great to icky, but their coffees, lattes, and espressos are still light years beyond pretty much any other coffee served at WDW.
Again, my best advice if you can manage it is to bring your own and brew it fresh in your room.