We spent 3 weeks in a town, Überlingen, on the NE shore of Bodensee last summer. You've gotten some good suggestions from people so far. We only spent part of a day in Konstanz, which felt like a big city compared to the other lake towns. We went there after seeing Insel Mainau, which was wonderful and I too recommend. Use Konstanz as a good ferry hub (you can buy multi day passes) and explore the other small towns like Lindau and nearby Friedrichshafen for the Zeppelin Museum.
If you like wine and wine tasting, I recommend taking the ferry to Meersburg to see the two tiered town in the vineyards. The TI has a map of walking trails through the vineyards. There are nice places to wine tasting in town too. Meersburg can only be reached by ferry, bicycle or car, no train station here.
With 3 days to explore, you'll have some great choices, enjoy!