Espresso was a big concern of mine also, being from the Pacific Northwest.
We just got back from our WDW trip from Nov. 9-22.
We stayed at POR and Polynesian.
POR - nothing. Supposedly there was a push button espresso machine where they sell the baked goods at the food court but it was out for repair and the lady said was being delayed - they had no idea when or if it would be back. It's still advertised on the board but it's not available.
POLY - espresso counter on top floor of Grand Ceremonial House near doors where you exit/enter from the monorail - it is also right near the Kona Cafe. Although the espresso drinks are made from a push button machine the CM operates, they were semi-decent IF the right person did them. Don't ask me how someone can mess up a push button machine but one CM managed it on two different days. One was extremely weak and the next time WAY too strong. Maybe the machine is fickle depending on whether it is overworked. This one is a hit-or-miss.
At the GF Cafe, my sister ordered a cappucino and when it arrived, the foam was topped with cinnamon in the form of a not-so-hidden mickey.
Room service at the Polynesian, you CANNOT get Kona coffee - only in the Kona Cafe. Room service pot of coffee is Columbian. Nothing special but not that horrible Nescafe garbage.
MK park - forget it. Get the espresso somewhere else before you get to the park.
Epcot - has Fountainview Cafe which is a real person using a real espresso machine and packing the fresh grounds themselves. Epcot also has two carts we found that seem permanent. They are also the real deal, not a push button machine. One is when you walk through Innoventions towards Mission Space - it's to your left immediately after you get through the Innoventions breezeway. The other cart was between Canada and England in the WS.
We were also happy to find a similar cart right outside the entrance to AK park. To your right when you get off the parking lot tram.
MGM we go to Starring Rolls Bakery right next to the Hollywood Brown Derby. This one we can't remember if it is a push button machine or if they pack the grounds themselves, but the beans are ground fresh there. I did see the one after you exit the shop at TOT but didn't check it out.
Typhoon Lagoon also had a cart. When you get inside, past the area where you rent lockers and towels, and then you cross the bridge toward the main wave pool, it is a bit more toward the right side of the park but not very far. Again, can't remember if machine or hand packed but I think hand packed grounds.
DTD - Fourty Thirst Street does not have a store anymore, but they do have a cart. Park/enter DTD near the AMC theatres and Planet Hollywood walkway and just walk straight back toward the water. This is the real deal stuff.
I asked at Epcot and at TL. I also asked about Fourty Thirst Street. Some CM's have no clue but just keep asking until you find someone who's in the know and will point you in the right direction.
The carts I described (Epcot, AK, TL and DTD) were the best we've found at disney. I would go to one of them before I would go to the Kona coffee bar or anything at a food court. I also prefer them to french press coffee. I save the french press (GF, Kona, Jiko's/Boma) to have after dinner with a sweet dessert. But for AM espresso to start the day I would definitely find one of those carts!
Rhonna
PS - we had incredible weather and low crowds.
