Which can be a medicinal spring, but also other potentially beneficial effects [2], there are towns on the sea, which have the prefix "Seeheilbad" [3], which is purely based on the positive climatic effect of the nearby sea.
And then, this is Germany after all, there is a long list of other boxes that need to be ticked, see [4].
[1] https://de.wikipedia.org/wiki/Bad_(Kurort)
[2] https://de.wikipedia.org/wiki/Heilbad
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.
"In modern German, Baden is a noun meaning "bathing"[4] but Baden, the original name of the town, derives from an earlier plural form of Bad ("bath")"
