The place you're referring to is called Club Cool. This is one of my most favorite hidden gems in all of Walt Disney World.
Club Cool is in Epcot, tucked away in a little corner near the main Future World Fountain on the Innoventions West side. From the outside this looks like a little gift shop sponsored by the Coca-Cola Company, featuring Coke-themed merchandise. Club Cool is a shop, but it is so much more!
Inside there are about 10 stations that each offer 8 free fountain sodas. There are nearby dixie cup dispensers. You can help yourself as many times as you want, drinking as much free soda as you want. There is one catch though, none of the soda is American. What's offered here is Vegita Beta from Japan, Fanta from Costa Rica, Mezzo Mix from Germany, Lift from Mexico, and several others. These are very popular Coca-Cola Company brands in these countries, but they taste more than a little foreign to most American palates.
On our last trip to WDW, my girls spent nearly an hour tasting, mixing, comparing notes about, and yes, spitting out (into the well-placed trash cans) the various soda flavors. I personally found one of the sodas revolting, most tolerable, and two delicious. I'll let you figure out which was which :-)
Oh, and if you want a good-old-American Coke, they sell those by the bottle at Club Cool for about $2.50.