Kenting National Park is a huge park located on Taiwan's southern most points. There are several things to around the area so plan to spend at least a day there. The walking paths that hug the coast line are very nice but go early before the temperatures get too hot. Some beaches allow swimming but this can change depending on tide strengths.
Renting a scooter or car is advisable as buses seem to be rare in this area. You can also find buses which run from the Kaohsiung Bus Terminal which is a 2.5 hour ride.
Colin Roohan traveled to Taiwan courtesy of Taiwan Tourism, Ritz Tours, and Eva Air. His highlights are part of AFAR's partnership with The United States Tour Operator Association (USTOA), whose members provide travelers with unparalleled access, insider knowledge, peace-of-mind, value and freedom to enjoy destinations across the entire globe. See more about Colin’s trip at the USTOA blog - http://ustoa.com/blog/category/afar/