Lake Constance

My only experience is Lindau which I think is a great place to visit.

Seconded Lindau.

Konstanz itself, if you are that end of the lake don't miss Insel Mainau (see here: https://www.mainau.de )
Stein-am-Rhein (west of Konstanz, not on the lake) is very pretty and worth a visit.

Bregenz is also nice. Lots of other nice towns to visit, too many to list.

In addition to Lindau take a look at Überlingen too. We stayed in Überlingen for 3 weeks and loved it. We visited several of the lake towns and these two, Lindau and Überlingen, had the most tourist infrastructure and beauty. You can’t go wrong with either town on the shores of the Bodensee.

We biked around Lake Constance over 6 nights in 2012. Our favorite overnighters were the town of Constance and Lindau. Meersburg is very nice also, but we didn't spend the night - just did some sight seeing. If you enjoy biking at all you should consider renting a bike for a day or two.

In Lindau we stayed at the Hotel Ruetemann in a room facing the lake with a balcony. It was probably one of our most treasured hotel stays ever!

Thanks to all of for the input! I do love to bike and plan to rent one. I’m so looking forward to this trip.

We stayed in Friedrichshafen and visited the Zeppelin Museum. It is a very interesting small museum and I recommend it. Distances are small enough that you could visit the Museum from any of the towns mentioned. I also second the recommendations for the Insel Mainau, Meersburg, and Stein-am-Rhein.
Have a great trip.

I stayed in Meersburg and loved it, but I think Lindau makes a lot of sense for your plans before/after your stop at Lake Constance. And, as others have noted, Lindau is a picture-perfect town. I really enjoyed my day trip there and would happily stay there on a return trip to the area.

Thanks again to all of you for the input!!