The Bodensee region makes day trips easy. Konstanz, the largest city on the lake, is 45 minutes by steamer or train and has a well-preserved medieval old town, the Münster cathedral, and the archaeological museum. Ravensburg, 20 km north by train, is a beautifully intact medieval trading city with its famous towers and the old linen-trading quarter — one of the most underrated towns in southern Germany. The Lake Constance page gives an overview of the whole Bodensee area including Meersburg (the castle town opposite the ferry landing), Lindau (the island town at the lake's eastern end), and the Austrian shore at Bregenz.
For those with more time, a circuit of the whole lake by bike — the Bodensee-Radweg is 260 km — takes four to six days and is one of the classic European cycle routes.