Budapest has a lot of bathing, with all you can find on this site: www.budapestgyogyfurdoi.hu.

The most basic, in my view:
Szécseni Fürdő (website)
There is a large number of indoor and outdoor swimming pools with medicinal water, as well as one outdoor sports pool. Use of the sauna at no extra charge The cost of the ticket varies depending on the time of visit. There are morning tickets, evening tickets and all day tickets

Király Fürdő (website)
Historical bath (Turkish bath) only with medicinal water. The cost of the ticket is also different, depending on the time of visit. The price includes use of the jacuzzi and saunas.

Rudas Fürdő (website)
6 pools with thermal water and 1 with plain water, use of the sauna. Here the days are divided into women's and men's. Women's day - on Tuesday, men's day - Monday, Wednesday, Thursday, Friday. Night swimming from 22:00 - 04:00, on Fridays and Saturdays. Joint swimming on Saturdays and Sundays.

Gellért Fürdő (website)
Several pools with thermal water. The swimming pool is also designed for tourists with disabilities: The cost, as in all bathing suits, varies depending on the time of visit.

Practically in all the baths there are additional services, massage, various procedures, solariums . The site of the bathhouse has all the information on services, prices, working hours, etc.