I was there as few years ago, the spa in the big, posh, Gellert Hotel was pretty good. Men and women are separate, but there is a common swiming pool. Think 1900's marble and gilt, dolphins spouting water, mahogany panelling and so on. Quite gay friendly (a guy tired to pick me up, and saw another having a wank in the showers), but not a place to go to if you are looking to get screwed.
BTW, Budapest is a beautiful city. They still have Viennese style cafes, violin trios to entertain.