The Swiss coast of Lake Constance has fewer attractions and is more boring than the German one. The most worthy object to visit is just Sankt-Gallen, apart from the Stein-am-Rhein and the Rhine Falls, which are actually on the Rhine, and not on the lake. Although from the other end of the lake I would not go for him alone.
The city is located in the hills behind the lake, 15-20 minutes by train from the nearest coastal town of Rorschach. There is absolutely nothing to watch in Rorschach. Its main attractions are the ferry to Lindau and the funicular to the nearest mountain.