Several counter service restaurants in Epcot Future World offer self-serve beverages. They can be found at Electric Umbrella and Sunshine Season Food Fair in The Land pavilion. In the Magic Kingdom self-serve stations are available at the Be Our Guest restaurant and at Tortuga Tavern. At Animal Kingdom, Restaurantasaurus offers a self-serve beverage station. At Downtown Disney self-serve soda is available at Earl of Sandwich and Wolfgang Puck Express. Many of these stations seem strategically placed as far from the seating areas as possible and can be easily forgotten. Still, one should be able to get free refills at these dining spots.
I also know that Backlot Express @ DHS has one, too.
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