Kenting is cool. Definitely pay for high speed rail if you're traveling south; we made the mistake of being cheap and it took like 6 hours to go south whereas it was like 1.5hr to come back.
This was also a really cool place to go. Rented electric bikes.
http://travelkaohsiung.com/places-to.../cijin-island/
The U-Bike program is pretty cool as well; used it in Taipei. You'll need a local SIM. I had the pleasure of teaching a local how to sign up for the program :P
We also went to the Wetlands during QingMing
http://travel.taichung.gov.tw/en-us/...Gaomei-Wetland
We also went here
https://www.tripadvisor.ca/Attractio...ge-Nantou.html
The last two places listed: we were taken there by a cabbie who we paid for a 10hr day. I don't remember what the cost was... It was pretty cheap though. I think it was like $70 each for 3 of us and those were some pretty distant places to be going to.
Don't forget
DTF dumplings!
Of course we also went here:
https://www.tripadvisor.ca/Restauran...ng-Taipei.html
Disclaimer: I speak Mandarin / some Taiwanese so maybe what I consider as good activities are not so much good for you.