I found Tainan to be interesting for a couple of days. As a day trip from Taipei, I'm not sure it's worthwhile given the location of the HSR station with relation to the city. How well are you and your parents able to get around? I did a lot of walking in Tainan but I am sure you could arrange a car and driver as well.
Taipei is a big metropolis with lots to do. If you haven't been to Taroko I agree that is worth doing. I did it as part of a long weekend trip with my own guide/driver. The drive from Taipei takes a while.