I've seen several different threads about this
MK is a dry park.
DHS, besides the restaurants, I really haven't heard much about any places to drink there.
AK - everyone has suggested the Dawa bar. Yak and Yeti also has a CS with some drinks, and I also think the TS has a bar.
Epcot - Have you heard of 'drink around the world?'. Depending on what you like, the list of favorites goes something like this
Mexico - La cava del Tequila (lots of fun margarita drinks)
Norway - Viking coffee (with baileys) or beer
China - (Joy of Tea Stand kiosk)Mango Gingerita, Canto Loopy, Peach Snapl orGreen Plum Bao Bing
Germany - Beer of course!
Italy - Peach Bellini, Limoncello or wine
Japan - Hot Sake
Morocco - kiosk (they have sultans colada or a daquiri)
France - EVERYONE has suggested the Grey Goose Slushie or the Grand Marnier (Both are good!)
UK - Welsh Dragon or Strongbow Cider
Enjoy your drinking!