The cheapest beer is at the Hess Markets gas stations.
There is one across from Downtown Disney that is easy access if you don't have a car. (Take a Downtown Disney Bus from your resort, get off at the 2nd stop, turn right as you exit the bus instead of left. Head towards the traffic light and crosswalk. You can't miss it.)
There is one across from the Boardwalk.
There is one at the Car Care Center as you exit the Magic Kingdom parking lot.
The resort shops sell beer by the six pack out of coolers and they are less than the bars/food courts.