We have been visiting Beitou quite a bit recently so found this park with a free hot spring foot-soaking pool.
Here's the foot soaking pools:
The address is: No. 48, Zhuhai Rd, Beitou District, Taipei City, 112, type in Fuxing Hot Foot Spa or 復興公園 into google and you should be set. It's right next to the xinbeitou MRT station.
My kids really liked this large park with a good sized sand pit that's covered which is a rare site in Taipei parks.