Originally Posted by globetrotter
1. you have to see the national art gallary, one of the 10 best museums in the world
2. soup dumplings
3. go to the top of the tallest building there, for a short period, I think that it was the tallest building in the world.
that's all I got
I agree with all of this, but to elaborate a little...
The art gallery that I'm sure he's referring to is the "National Palace Museum - 国立故宫博物院", and anyone who goes to Taipei should be required to go there. It has an incredible collection of Chinese historical artifacts, and is the only collection that rivals (exceeds?) those in Beijing.
For the soup dumplings I recommend "Din Tai Feng - 鼎泰丰. There is one not too far from Taipei 101, so you could probably combine them in to one trip.
The night market is also a must (I forget the exact name off hand but if your gf can speak Chinese any cab driver will know it). I don't know what you like to eat, but there are tons of good snacks there.
There is also a really good seafood market with really fresh fish that you can eat cooked, raw, whatever, all prepared on the spot too. I can't for the life of me remember where exactly it was though.
The mountains also have some cool tea houses. For nightlife there are some pretty sweet clubs, KTVs(like everywhere in Asia), and some cool lounges up in the mountains.
Hope that helps
Hope that helps.