Back in April I paid VND130,000 to use the swimming pool at The Grand Hotel on Dong Khoi. Gets busy when the day tours come back in the afternoon. The New World Hotel near Ben Thanh market has a much bigger pool for a much bigger cost. From memory it was around VND400,000, maybe a bit more but worth the splurge as I was stuck in town on a dental visit. I would avoid it on their pool party days though. Back then it was a Saturday.
I've been told by an expat that there is a good public pool out near the zoo in Dist. 2. Hope this post isn't too late.