Here is the latest hospital list from the Taiwan CDC:
https://www.cdc.gov.tw/File/Get/_okJOR9WegmNO-cIiSK5zw
I got mine at Shuang Ho Hospital – next-day result for 5,800 TWD – no appointments are needed. Just arrive before 10AM on weekdays. I was in and out in 15 minutes. I highly recommend them.
Antigen testing is much cheaper: 2500-2600 TWD. Unfortunately, it’s only available at Tong Yen Hospital in Hsinchu and Landseed Hospital at the Taoyuan Airport.