One of your first stops should be The Jiangs Cultural Park. Here, you'll be able to find your bearings and get some great ideas before you start exploring.
This tourist information center is situated in Taoyuan District, a place that has lots going for it! Chung Yuan Christian University, Taoyuan Night Market, and Taoyuan Arena are other worthwhile sightseeing choices nearby when you've had your fill of The Jiangs Cultural Park.