Drinking around the World is one of my favorite topics. Most of these places also have some yummy non-alcoholic drinks and stuff to do other than drink. Here are my favorites:
Polynesian resort - Lounge attached to O'Hana. This has the best Mai Tai outside of Trader Vic's. Lotsa other fruity drinks served in cool glasses or pineapples. You can get it and sit in front of a big TV in the lounge, catch a table in the hall and listen to the eukalele player, or get it in a to go cup with a straw and take it onto the beach to watch Wishes or on the monorail for a quick ride.
Contemporary Resort - California Grill bar. My favorite here is the Cosmopolitan martini. Grab a drink, or two, and head out to the balcony to get a bird's eye view of Wishes. They pipe in the music. I know one can only go up there now if you have reservations; but the bar is also accessible. Just tell the hostess you want to belly up to the Cali Grill bar for a great martini, and you won't have a problem.
Contemporary Resort - The Wave. Haven't been here yet, but I have seen the wine list. This place specializes in wines with twist-off caps. Helps with the world's shortage of cork. Try Jester Shiraz.
Boardwalk Inn & Villas - ESPN. Nice arcade. Decent food. Good place to catch a beer and the game.
Boardwalk - Jellyrolls. Nuff said already.
Boardwalk - Leaping Horse Libations. This is the main pool bar at the
DVC Villas. Try their signature mixed drinks.
Animal Kingdom Lodge - Jiko is not only my favorite restaurant, but has an awesome wine list. This is the largest list of African wines in the country. There are also some really nice teas, for those looking for something good sans alcohol.
DHS - 50's Prime Time Cafe has a nice bar. You can get a drink in a to go cup here as well. My favorite here is best in chillier weather. Get hot cocoa with a shot of Rumplemintz or peppermint schnapps. The screwdriver and VW Manhattan is good, too.
AK - The little bar in Africa has awesome hot weather drinks. This is one of the only places I will drink a Pina Colada. Theirs are mighty tasty. You can sit in the shade, enjoy your drink and watch a show. Typically there will be live entertainment here, such as drummers, African dancers and African acrobats at various times of the day.
Epcot - I second each and every statement made here. Two additions, though. Try drinking around the World Showcase. There will be plenty to do in each country while DSis drinks. Rose & Crown and Germany have beer samplers. France, Italy and Germany have wine tastings.
Hope this helps.