I went to the Gellert spa, it was ok. Not in the main pools, but for the separate pools for men or women only there was a lot of nakedness, although that is optional. We didn't try the bit outdoor pool. Had a nice massage there. It is over the other side of the river from the main town though and not the easiest place to get to.
There is a very good underground and lots of trams and buses but you do need to know the system as apparently if you don't have the right ticket there can be a big problem. Back when I went we bought a booklet of so many one way journey tickets, but, if you had to change, e.g. two different underground trains on one journey, it was another ticket per change from what I remember. Once we knew the system, the underground was great.
I had the benefit of knowing some locals so they helped explain a lot to us. English is not so widely spoken, it is in restaurants and tourist attractions but not so much (that I found) in underground stations, taxis etc... so good to plan ahead and know what you need.
I can highly recommend the zoo, had a great time there.