Pohang, Buk-gu, Jangsung-dong - Pohang Oncheon
Unfortunately, they don't have a website and there's very little information on the internet about this spa. I'll leave you with the couple photos I tracked down, directions & a map, and a teensy bit of info.
Pohang Oncheon is North from Bukbu Beach, it's only a short taxi ride, or you can get the bus numbers 108 or 109 from the rest of the city to the south.
경북 포항시 북구 장성동 1518-1번지
Gyeongsanbuk-do, Pohang, Buk-gu, Jangsung-dong 1518-1
Open 24 Hours
Seems to be 4,000 for adults / 3,000 for children
(I can't remember exactly how much I paid!)
Wikimapia of Pohang Oncheon