You can find coffee in many places. Besides the restaurants ...
In Epcot: Try the Fountainview. They have all sorts of coffee drinks and great desserts. In World Showcase, try the bakery in France or the dessert cart in Italy.
In MGM: Starring Rolls (next to the Brown Derby) has coffee, soda, baked goods. Nice for a relaxed stop. Also, the Book Stop, which has coffee, cookies and books to buy.
In Magic Kingdom: Try the Bakery on Main Street and the counter service places throughout the park.
In Animal Kindgom: The Bakery in Africa (near Tusker House) is a nice choice for a quick cup.