We spent a long weekend in Lake Konstanz. We actually stayed right in Konstanz and took the car out to explore the surrounding areas. It's beautiful! You can also head over to Mineau Island, the flower island. We went in October and although it was beautiful, not many flowers/trees were in bloom. I'd suggest heading there in the Spring/Summer when you have a better chance of enjoying the flowers and their smell.
Mineau Island in October
If you're in the area, I would recommend a stop at Stein Am Rhein in neighboring Switzerland. See my post for more info.