Szechenyi, which is in a City Park on the Pest side.
Szechenyi is said to be the biggest public bath in Europe, and is famous for the chessboards set directly in the bath for the chess lovers. There are three good-size open air baths (pools), each with a different temperature. Despite it being another cold day in Budapest, the pools were enjoyed by lots of local people and tourists like us. I, being Japanese, tend to enjoy hotter baths(defnitely above 39 C degrees), but none of the three baths had a temperature that high. I suppose it was designed to be that way, so that people can dip themselves for a long time. In fact, we were in the water continuously for over an hour (well, we couldn't get out as it was freezing!), which I could never do in a hot Japanese bath, and most people were there before we got there and stayed after we left. The old men playing chess definitely had a plan to stay there and to enjoy their Saturday chess games in the bath all day.
You will need to bring your bathing suit, a towel, slippers, and maybe a robe especially during the cold winter time. Since we only brought our bathing suit, we ended up renting a piece of cloth that they called a towel. It didn't work out that well. Also, the facility is not like a spa and more like a public pool. You would smell sewage, and you definitely don't want to walk through the facility with bare feet like we ended up doing. But, the bath itself is great, and we felt really good after dipping ourselves for nearly 1.5 hours.