Do I need to book a room from a hotel?
Are there any public ones?
What is the cost?
Should I expect nudity in saunas?
There's a Thermal Spa Centre!
The new thermal spa centre, on the opposite bank of the river Passirio, was opened during the 1970’s and is furnished with the most modern equipment for therapeutic treatment. It also houses an indoor swimming-pool filled with thermal water and the natural radio-activity in this water has a most beneficial pathological effect. The spa centre is open all year round and specialises in a vast selection of curative treatments.
Prices range depending on whether you want a spa, a bath, and for how long. This page has a list of prices.
There certainly doesn't appear to be any indication of nudity.