For me, I would go scootering there at least once. It depends on your comfort level. In the evening, it's kind of like chaos to be on a scooter though. If you're going to scooter, it is highly recommended to buy travel insurance, and don't give up your passport when renting. There are smaller scooter rental stalls that will rent to you for straight cash or International Drivers Permit.
Do Kenting park, if you're into nature. It's maybe a 3 day thing. I think it's like 3 hours each way from Kaohsiung.
For me it'd be:
day 1: check in, rent scooters, go here (
https://goo.gl/maps/Cgqfg1azdnw ) and talk to the tourist info people they'll have some suggestions depending on what you want to see, get sunset pics
day 2: wake up early, sunrise pics, cruise the coast and mountains. night market.
day 3: Kenting national park
day 4: check out, grab the bus back to Kaohsiung.
When I went, I combined day 2 and 3, and didn't have time to see it all. I saw about half the park.
Other than that, there isn't really much else to do. The scenery there is really nice. There's a beach there where, Life of Pi, was filmed, it's pretty popular with the Chinese tourists.