First, you'll need to consider renting a car to get to some of the nicer spa areas which are not that easily reached by public transport.
Second, if you're trying to relax and enjoy the hot springs, then I don't suggest you go to the natural hot springs outdoors that require you to change in the car and walk around stinky after your bath
Having said that, all of the spots that still have an open natural hot springs outside ALSO have a hotels and wellness centers nearby that use the same hot springs but offer the possibility to stay overnight as well as enjoy spa services like massages, facials and other treatments. Most have restaurants to fully relax the entire day/evening.
The nicest ones you can try out are the Saturnia hot springs which would give you a chance to try both the "free" natural waterfall as well as the services/hotel stay right next door. If you already know your dates, you could already book online here (affiliate link).