The plural would be "Bäder", but I'm not aware of any town using that plural form. It would be very strange, too, because a town is a single entity.
Baden-Baden is the only one I know that comes close, and https://en.wikipedia.org/wiki/Baden-Baden#Name explains how it got that name. It's not the spa prefix, but part of the name proper.
Also, "Baden" is a region in the south-western state of Baden-Württemberg that probably has lent its name to other towns.
It is home to one of the two big dialect families in Baden-Würrtemberg: Badisch, the other being Schwäbisch/Swabian.