Tainan is a city in Taiwan.
There are a number of ways out of the city going south. Basically you want to get onto an entry ramp onto highway 1 or 3.
Ollie used the on ramp pictured below to hitch south. It was a non-ideal location (as it's in the north east of the city) but he was offered a lift there to just took it. You can hitch from just in front of the car repair shop here (which is at the 'x' in the map pictured below). He had to wait for 30 minutes and eventually got a ride to Kaohsiung. 30 minutes is quite a long time to wait for a hitch in Taiwan.
Here's what it looks like there.