sorry, are you looking for a place to practice wall climbing? or you looking for a gym?
climbing walls are at a few SAFRA locations: one of the biggest ones is in Yishun. The nearest MRT station would be Khatib and then a 15 mins walk, or Yishun MRT and a few stops on 812 bus.
Look at the SAFRA website. You can become a member of the adventure club and then you get discount on using the walls. The ones at Yishun is going up to 25m. All outdoors.
Hope this helps!
I don't know any gym that has climbing walls