Is a pretty famous waterfall in Switzerland & the most powerful in Europe. The Parking costs a little bit, but entrance is free. You can get there pretty easy by train, or it's 30 min by car.
Reichenau is a very cute Island in the Lake of Konstanz. If the weather is nice it is a great place for long walks and a swim in the lake.
Is another Island, that is kind of like a park, kids really enjoy it. It's called the flower Island, there is butterfly house and a nice water playground for kids. You do need to buy a ticket though.
Is a very famous and beautiful lake that connects Germany, Switzerland, and Austria. You can swim or rent a boat pretty easily.
Is a cute city, right at the lake. There are some good cafes and restaurants right on the water. Scroll down on the link and then you find some specific recommendations for Konstanz.
One of the old Volcanos with a castle ruin at the summit. Here are the other Volcanos: - Hohenhewen (20 min. drive) - Hohenstoffeln (10 min. drive) - Hohentwiel (10 min. drive) - Hohenkrähen (15 min. drive) - Mägdeberg (5 min. drive) And some more (Ask Esther for hiking tips and routes)