Hengchun, which is 10km from Kenting, has an airport serviced by one Uniair flight from Taipei, 3 times a week. For some reason, its not a popular option and so there are frequent cancellations when the minimum number of passengers needed to make the flight isn’t reached. Perhaps it has to do with the gale force winds that blow on and off throughout the winter months. Prices are between NT$1800 and $2200.
Kenting is not serviced by either the high speed rail or conventional rail so if you are not flying directly to Hengchun or traveling with your own vehicle, you will have to first get to Kaohsiung. You can do this by rail, high speed rail, bus, or air.
Flying to Kaohsiung is quick and relatively expensive. You can often just show up at Taipei Songshan airport 20 minutes before the flight and buy a ticket. You can also arrange tickets at Taoyuan Airport when you enter Taiwan.
High Speed Rail is probably most painless way to get to Kaohsiung. You get off in Zuoying station and it takes less than 2 hours from Taipei .
Rail is more expensive than the bus, slower than bus, air or rail, and less comfortable. Sometimes, it just works out best though. Schedules here
Buses are cheap and very comfortable. Many buses offer reclining armchairs (often with a massage feature), blankets, complimentary drinks, and a personal TV at your seat. It takes around 5 hours but its a cozy 5 hours. The Ho Hsin and Ubus companies are both good. Expect to pay about NT$600
