I thought the National Palace Museum was phenomenal. It's too bad there isn't more display space. It can get very crowded with all of the tour buses. I enjoyed it without an English tour. They also have those recorded tour things available as well.

I liked the Baoan and Confucius temples. Go in the evening when it is more atmospheric.

I find the whole betel nut thing disgusting.

Make sure you try the curry beef noodle soup.

You really haven't got much time there. There is a very nice museum called the National History Museum at the botanic gardens that has a great collection of stuff. Old Chinese artifacts as well as more contemporary art. http://en.wikipedia.org/wiki/National_Museum_of_History