How much beer do you plan to keep on the room?
I'm only asking because, to my knowledge, the Value resorts (All-Star & Pop Century resorts) are the only ones that don't get refrigerators in the room standard. Meaning your beer will be warm, which for all I know you like, or can live with if it means saving money. Getting a refrigerator will cost you an extra 10 dollars a day, which would offset the money you're saving getting beer at the Hess station.
Oh, and for a lot of people, "7-11" is ubiquitous for "convenience store" the same way people say "Xerox" instead of "copy," "Band-Aid" instead of "bandage" and "Tivo'ing" instead of "Digitally Recording." So when this person said there was a 7-11 nearby, I'm sure they didn't mean to confuse you.
I also think there's a Goodings supermarket in one of the back entrances to WDW, at Hotel Plaza Blvd (I think that's what it's called). I'd say if you need beer, get a cab, stock up with as much as you can in that one trip (and get any other snacks you need.
If you really want to save money on beer: Don't eat. At all. This way one beer will go right to your head no matter HOW expensive t is! :lol: