Taipei is already a free-for-all. Driving against traffic is relatively common, particularly with scooters, bicycles, etc., so nothing out of the "ordinary" here. The biggest difference down south is that helmets are optional. Red-light running can be more common (rare in Taipei except at night). Possibly more drunk driving and complete cluelessness due to even more lax enforcement and lower traffic volumes although stuff like when on a rainy night a car with headlights off that was stationary on the shoulder suddenly starts making an illegal U-turn right in front of approaching traffic can happen in Taipei as well.

Expect no sidewalks, no traffic lights for pedestrians, and larger streets and especially bridges to be tedious to cross on foot. Often you might be pleasantly surprised though, it really depends on the particular area. Central parts of Gaoxiong have significantly improved and are on par with Taipei now, possibly even more walkable. Other cities are slowly catching up too.

If you like repurposed industrial sites, you should definitely see Pier 2, and also the Qiaotou Sugar Factory in Gaoxiong. 85 Sky Tower is a landmark similar to Taipei 101, visible from much of the city. Also, check out Huashan 1914 Park in Taipei if you haven't had the chance yet.

I know there's something in the spirit of the above in Taizhong. Not sure about Tainan. Someone else can hopefully provide the details.