Taichung
I grew up in Taichung and still can't clame I know it well. Until I left I didn't know how unique this place is. It has a calm weather, people are nice. Taichungers live a confortable life style, a bit slow tone, aren't as urbanized as people in Taipei, nor as enthusiastic as the southern Taiwanese. The phrase "Taichung" actually means "the middle of Taiwan", which and geographically true, and also shows the city character.
Taichung is a great place to live in, but probably not to exciting for travellers. "Where to go to in Taichung?" That's a difficult one. Taichung has two fantastic night markets that are famous island wide, Taiwanese could come to Taichung just for night markets. But unless you're a true night market fan, the night market in other cities should be enough. We have the Taiwan art museum here. We have the Taiwan natural science museum here. All the mountains and resorts are near. Maybe that's all.
Bubble tea (Pearl Milk Tea) came from Taichung. I think they still have the best here, so if you come to Taichung, don't forget to check it out! Chun-Shui-Tang(春水堂) is my favorite place to go, their website has very little english but at least you have the phone numbers there.