Enjoy the cheap shopping, soak in the springs, and EAT EVERYTHING!
My wife and I can't wait to go back to Taipei. It's surprisingly English-friendly, the transit system is reliable, the night market culture is lively and the food is delicious! It's the first big city that we've been to that didn't just feel like another big city. Taipei is a great choice for budget travellers, too. The cost of living is quite low.
Insider Tip:Go to the night markets on weekdays--weekends are super crowded. Also, if you go to the National Palace Museum, you can avoid most of the tour groups by coming at about 4:00 or 4:30. Most of them leave at about 5:00 to go for dinner, and then you have 90 minutes to enjoy the museum without the surging crowds.