I've been to almost every state in Taiwan (Taipei all the way to Ping Tong), but I like Taichung because it less hectic than Taipei, and a half hours ride and you are out of town to those charming little farms, scenic mountains and friendly locals (been to Miaoli often too).
So you got all the convenience of the city with nature not far away.
And best of all, cheap cheap cheap...
You pay like something around NT$8000 for a duplex suite (one bedroom though). My sis got the same thing in Taipei for like NT$17000.
The downside I think it is the food, can't seem to find authentic western cuisine here, most of it are catered to the Taiwanese palette. So I have perfected the art of cooking with a toaster (no kitchen at my place)
Oh yes and the crazy bikers...