I do pack my little Farberware percolator and bring my own coffee with me.. Green Mountain...that is how bad the coffee is at WDW..
Some restaurants do offer French Press, two that come to mind, Spoodles for breakfast, Citrico's for dinner, and whatever ones people say offer it, they usually know as we all search out the best coffee on property..
Also, thank God, Swan and Dolphin offers Starbucks......so if you need a decent cup to go, I would go there. In the morning, at the bar in the Dolphin, they have coffee and pastries, and usually in the front area at the Swan, they do the same.. Also, Picabu and their restaurants serve Starbuck.