At following places you can find some public toilets in the town center of Baden:
At the Rathaus/town hall (D2, entrance in the courtyard beside the shop Tabak Trafik), in the Kurpark (D3, in the area right beside the main entrance), at the Grünen Markt (CD2, nearby the car park for buses), in the Doblhoffpark (B2, small building beside the café). The toilets locations are marked with a WC symbol in the PDF town center map Baden.