When you say "the park", I assume you mean Kenting National Park? There is indeed a lot to see in that region besides that park, and one of the first things to mention is that there are other parks and nature reserves around the Kenting area. Sheding Natural Park, Maobitou Park, and the Kenting Long Keng Ecological Reserve are all worth including as part of your itinerary.
If you're staying in a Kenting villa like this one, it's a good idea to drive out during the nighttime to enjoy the local night markets. There are many towns around the Kenting region, and their night markets are home to all sorts of local specialties and interesting street foods.
Of the local towns, Hengchun stands out as being home to both a sprawling night market and a wide range of interesting historical and cultural sites. Hengchun is the only fortified city in Taiwan that still has all 4 of its gates intact. Some of them are still in use.
