The Bodensee is a wonderful area often overlooked by American tourists - but not by German tourists. Wherever you choose, I'd book as soon as possible.
I've stayed in Lindau and Meersburg and loved them both. Lindau feels more Mediterranean and is very elegant and charming. Meersburg has an old city on the hill (above the lake) with a castle and feels a little more traditionally German. Meersburg is closer to the southern Black Forest but it's a significant (although scenic) drive from anywhere on the lake.
There are wineries along the lake itself, or for a long day trip into the Black Forest you could visit the very famous wineries of Baden, particularly this one hillside that is just across the border with France that is famous for being the sunniest part of Germany. The wines from that specific area are very well renowned but I can't remember the name at this moment.
As for things to do, aside from exploring Meersburg and Lindau (whichever you stay in, you should visit the other), there's the Zeppelin museum in Friedrichshafen, Mainau island, beautiful swimming beaches in various places if the weather agrees, a historic abbey, and a bit further away the Rhrine Falls in Swtizerland.