All the restaurants in the Swan and Dolphin do not take the DDP. We didn't go to any sit-down restaurants there, but one afternoon I walked over there from the Boardwalk Resort when we were spending the day by the pool, and I grabbed a burger from the Picabu Buffeteria. It was made to order, fresh and delicious! I wanted a small one so I ordered from the kids' menu for myself. Definitely way better than the burgers in the theme parks, perhaps because it was made fresh!
Other places I know of that don't take the DDP are Fulton's in DTD, Bistro de Paris in Epcot, Ghirardelli in DTD, Bongos in DTD. I'm sure there are some more I am not remembering.
By the way, many of the places I mentioned above do accept the Tables in Wonderland card. So if you are either a FL resident or an AP holder, you can purchase this card and it will give you 20% off everything including alcohol. We used it in July and we loved it!