If you're anywhere near Zhonghua, you should definitely go to the amusement park there. They have a few roller coasters, they're really nice. Like 10 times better than Lagoon. And if you're anywhere... Every town has some kind of waterfall or hike you can go up to.
If you go to Taiwan, the best place to visit is definitely the capital Taipei. Taipei is just so amazing. There are so many different historical places you can go, like the National Palace Museum. It has the greatest collection of Chinese stuff there. So you should definitely visit there. There are some museums in Taipei. Also Taipei 101 is for sure the best place to visit. If you ever go, make sure you buy the ticket to the top floor. It was definitely worth it. You can see the entire view of Taipei. And also Taipei has a lot of different restaurants to visit. If you love food for sure, you need to go to Taipei.
There's so much to do. I was in some of the Xiangxia areas, which is the most rural areas in Taiwan, and I was still able to find things to do. There's stationary stores where you can go buy things, there's clothing stores. Always, there's markets in every town. There's lots of tourist areas you can go to.
There's great hikes almost everywhere, like in most areas you'll be in. You'll have different cultural areas you can go to and learn more. Whether you're in Taipei or Hualien or on the west coast in Taoyuan or Toufen, there's great places to be regardless of where you are.