Hooters is an interesting place to go. Of course, the girls don't have any hooters, but they are still dressed in the same outfits that the Hooter Girls in the states wear and try to flirt the same way too. The layout of the restaurant and bar, and menu are the same as in the states, but the atmosphere is very different.
Also, try a tour of Taipei 101, the world's tallest building. That's good for 1/2 day. Try to go on a clear day, though.