for a 5-day trip we spent the first day at Taichung (Taroko mall which had jumpin gym type play area for kids which my 3-year old didnt wanna leave) and then night market. The next day picked up car for 2 days (IWS rental in Xitun highly recommended for reasonably priced but newish cars) and drove to qingjing farm in Renai where we stayed another night. The 3rd day drove to Puli (there was a wonderful waterfall on the way can't recall the name) , and were awed to see the sunset from the sunset point. The 4th day we returned to Taichung and explored the city further with the next day we flew back. I had never driven on the right before but bit of patience and a fantastic in-built navigation system helped a great deal.
Different people different preferences but I wouldnt prefer taipei as it's not much different from HK. Being closer to nature is what I intend to whenever I leave Hong Kong for a holiday.