I know my husband had the BEST one in DTD, at Ghiradelli's! Mmmm, mmmm, good! Mind you, it was 98º in September, but that didn't matter. Also, the Disney hotels have some good specialty coffees in/near their restaurants. Just please promise you will not drink the "standard" Nescafe, OK? You swear? Have a great time!
I know there is a speciality coffee and patry cart in Epcot World Showcase, right at the entrance to the World Showplace, where Canada ends and the UK begins.