Taipei is admittedly an ugly city, but it has its charms. Taiwan is the best place to experience traditional Chinese culture and Taipei is definitely not a boring city!
Places to see: YangMing Shan mountain (bus ride from downtown), hot springs in BeiTou & YangMing Shan, night markets, teahouses, Longshan temple, day trips to Jiu Fen and DanShui, week-ends in Taroko gorges, Tainan, etc.
As for the food, Asians crave Taiwan's "small eats". You must try Ding Tai Fung's original outlet. The restaurant is well worth its reputation.