The Lucky Nugget Cafe is hidden around to the right-hand side of Big Thunder Mountain. The specialty at the Lucky Nugget Cafe is Western-style fried chicken, an item scarcely found in Japan outside of the occasional KFC restaurant in and around Tokyo. I personally find the fried chicken at the Lucky Nugget Cafe very tasty. My favorite item is the combo plate, which comes with a piece of chicken and several other fried items. You can order your meals with or without coleslaw (I suggest you order it "with").
There is a nice bandstand—called The Lucky Nugget Stage—next to the main seating area. Sadly they no longer have shows here. I particularly enjoyed the live Country and Western band they had a few years back.
The Lucky Nugget Cafe is a great place to eat, with food that's likely to please most Western palates. Because it's slightly out of the way, it's usually less crowded than most other restaurants at Tokyo Disneyland. There is outdoor seating near the Rivers Of America, which provides great scenery while you enjoy your meal. Remember to wave a hearty hello to the passengers of the Mark Twain Steamboat as it chugs by.