I struck out in South Korea, couldn't find a single traditional gym. Ended up doing lots of lunges and squats with water cooler bottles.
I found a gym while in a high rent district of Rio this fall, but they wanted 100 Reais a day ($40 USD)!!!!!! Funk that shit.
I found a hardcore powerlifting gym while in Germany - I was the smallest dude in there. But I was in HEAVEN!!!!. The gym goers were very cool to this dumb American, and the owner told me to put a Euro or two in the Leukemia jar when I could - no fees.
Never been to Taiwan. Good luck.