Bodensee (Lake Constance)

Hotel Rheinfels in Stein am Rhein is very nice. It's right on the river in the middle of town. From here it's just a short drive to the falls.
Also, if you like small towns good for strolling, Hotel zum Lieben Augustin am See in Wasserburg am Bodensee is a very good choice (http://www.hotel-lieber-augustin.de/).
If you prefer towns a bit larger then Meersburg and Lindau are great places to stay. Wherever you stay, be sure to visit Insul Mainau to see the acres of flowers, plus have lunch at the Swedish restaurant near the castle.

I found Lindau gorgeous... but that was the only town I saw, so I could not compare it to any others.

Friedrichshafen is the best base in my opinion. It's got the best infrastructure, all trains to anywhere in the area stop there, all scheduled boats stop there and there is even a jetfoil shuttle link between Friedrichshafen and Konstanz. What makes Friedrichshafen special though is that the lake there is at its most width. It's 14km wide (8.7miles) which is exactly the width of the strait of Gibraltar. Also the Alpine panorama on the South side of the lake is at its most hight which means the view there is even more breathtaking than from Meersburg or Lindau. Also Friedrichshafen has got plenty of restaurants (many of them on the lakefront), shopping, the Zeppelin museum at the place where Hindenburg and the others were built.

Meersburg! Just a short ferry ride from Konstanz itself. It has a lovely Altstadt, two Schloss, a great water front, good restaurants (Look up the Lowen) and is well placed to travel to other Bodensee towns by boat or rail. We stayed in Konstanz in 2002 - I wish I had know about Meersburg before so I could have stayed there!