Taichung is more spread out than Taipei or Tainan and walking alone will not cover the city. The metro (Green Line) opened in 2021 and runs from the southern HSR station up through the centre to Beitun in the north, passing the National Taichung Theater, Wenxin Forest Park, and the Calligraphy Greenway en route.
The city bus network (TCMS) is dense and cheap; the iPASS Taiwan smart card works on all services. The first ten kilometres of each bus ride are free, which makes day-to-day travel essentially free for short hops.
For Dakeng, Gaomei, the 921 Earthquake Museum, and the more distant suburbs, you will need either a taxi (cheap by Western standards, abundant), a hired car, or one of the touristic bus routes (Taiwan Tourist Shuttle). Uber works in central districts.