Konstanz has a very modern, excellent thermal pool and spa. The large indoor and outdoor pools aside there are jacuzzis and several water attractions for the kids, a bridge across the walking path by the lake leading into the lake there. There is also a separate sauna/spa area which I did not use as I didn't have enough time - it's said to be quite fancy. They also have a very good restaurant in the Therme (Seelig) where I had a nice light supper.
Admission is not exactly inexpensive. I paid 5.50 Euro for "Evening tariff", meaning from 8 pm till closing time - which is 10 pm, but you have to leave the building showered and changed at 10. A ticket for 3 hours for the pools was 9 Euro, 3.5 hours incl. sauna 16 Euro (!).
Cycling is one of the favourite activities in the region. There is an abundance of cycling trails, starting with the trail around the lake (Bodensee Radweg) which is flat and easy and goes through all three countries sharing the lake: Germany, Switzerland and Austria. Crossing borders is easy, you hardly notice. The trail is well marked, maintained and signposted. Along the trail natural sights alternate with picturesque towns. You'll pass beaches, beautiful Baroque churches, playgrounds for the kids, cafes and restaurants ... and so on. What more do you want as a cycler?
There are bike shops along the trail in each town in case your bike needs repair/maintenance.
Equipment: Rent your bike. I would not drag it on the plane (LOL), train or car to the region. Renting is inexpensive and the bikes are well maintained (judging from the bike I rented).
You can join all kinds of water-sport at the lake. It is also possible to make a day-trip to the alpes to go hiking. In summer it is very popular to bicycle around the lake.