If you are thinking about visiting Taiwan and you only have a few days, I want to suggest three really cool places  to visit. 

The first place is 花蓮. I think you should visit Hualien because it is beautiful landscape and weather is good. My favorite activity to do rafting and river tracing.

The second place is 淡水Tamsui . I think you should visit this place because have a lot of delicious food and you can see beautiful sunset. My favorite thing to do ride a bicycle and watch the sunset at the same time.

Finally, I also highly recommend that you check out 澎湖 Penghu. I think you should visit Penghu because you can play many water activities and you can participate Penghu Fireworks Festival. My favorite thing to do watch fireworks with friends

In closing: if you visit Taiwan, remember to visit 花蓮, 淡水 and 澎湖. They are great places to visit.