Other things to see and do:
Cheng Kai Shek memorial, Fine Arts Museum, and National Palace Museum
You can also rent bikes for about $2 US an hour and ride the paths along the river
The food at Hooters is horrible, but is an ok place to drink and sightsee. Also near the Hooters is the Shannon and Brass Monkey bars.
Avoid the local beer - it is laden with formaldyhide. Worst headaches you'll ever experience!

Have fun in Taiwan-on!

The Imperial watch shop is one of the best places in the world for copy watches of great quality. You'll pay for them but they are worth the money. Right out of the hotel about half a block.