I love a mineral spa and find Central Europe/Balkan countries gla good, low-key option. Confidently flights are cheap so can go a few times a year.
Bulgaria has loads and it is a beautiful country full of mountain ranges. Spa towns I have visited include Velingrad, Pavel Banya, St Constantine and Helena and Banya/Dobrinishte just outside Bansko. They are joining the Euro next year and it is a country I have fallen in love with. Slovakia also has lots of thermal areas, as does Romania (Transylvania is stunning) Serbia, Slovenia, Turkey and Slovakia. All very affordable, great food and beautiful scenery.
I am currently planning a solo trip country hopping after flying in Bulgaria next month. Many of my stop offs seem to be conveniently near to thermal/mineral pools! I often stay in small local guesthouses/apartments and pay entry into pools but often the attahced hotels have a half board package to make things easier.
I know you said not Hungary, but I love Hajduszoboszlo. The quality of the mineral water is incredible. All of the places mentioned are used by locals (often prescribed services as well as for leisure) and nudity is not the norm. Germany and Switerzland are very strict that no textiles are warn in the sauna zones so avoid if this would be an issues.