The "Lonely Planet Taiwan" guidebook really likes Taichung and has a pretty good map.
Lonely Planet recommends the Taiwan Museum of Art at 2 Wuquan W Road; the National Museum of Natural Science at 1 Guanqian Rd, off bus 71; and the "tea street" across the road from the sculpture park, facing Xiangxin South Road: "many classy restaurants and cafes that ... close around 10pm".
For budget accomodations, they recommend the Taichung Hostel, tel. 2372 1935, 400 Meicun Rd Sec 1, rooms from NT$1800 (single) / NT$2400 (double): "not a true hostel but a government-run hotel... large rooms, spotlessly clean" and the Fuh Chun Hotel, tel. 2228 3181, 1 Zhongshan Rd, just across from the train station, rooms from NT$500: "all rooms are fine."
Online, you can check out
Taiwan Fun's "Today in Taichung".