The old town is compact and walkable — everything between the train station, the cathedral, and the harbour is covered comfortably on foot in under twenty minutes. A car is a liability here: the streets are narrow, parking is expensive, and the useful parts of the city are all within the pedestrian zone.
For getting out onto the lake, the ferry is the natural transport. The BSB ferry network connects Konstanz to Meersburg (fifteen minutes, continuous service), Mainau island, Friedrichshafen, and further ports on the Swiss and Austrian sides. Day tickets cover multiple crossings.
Konstanz is a good city for cycling. The lake shore paths are largely flat and well-maintained, and the route north along the Rhine is pleasant. Bike rental is available near the train station. It is possible to cycle to Mainau island via the causeway, avoiding the ferry entirely.
The border with Switzerland runs through the middle of what looks like one continuous city — Kreuzlingen is directly adjacent. Swiss trams and buses connect the two sides, and crossing on foot or by bike takes a couple of minutes with no formalities.