Near Berlin Schonefeld Airport

Can you turn the car in beforehand? Then travel to Berlin by train and spend the evening there and take the train the Schoenfeld in the morning.

There are historical towns on the south side of Berlin if you want to consider them: Zossen, Großbeeren, Fürstenwalde, ie, historical in that they are connected to events in Prussian-German history. I've passed through Großbeeren a couple of times, haven't been to the other two.

Thanks for the suggestions. Magdeburg or another town on the Elbe look like possibilities also. We will already have spent several days in Berlin before venturing south to Dresden, Prague and Leipzig so something on that side is what we're looking for.

Wittenberg is not a bad choice, especially since it's a small town which makes driving easier. And the town is quite nice with a preserved centre and several sites related to Luther and the Protestant Reformation.
If you not that interested in history I would recommend Lübbenau instead, a small town in the Spreewald, where the river Spree meanders in thousands of small waterways through meadows and forrests. Lübbenau has a small preserved old town, a harbor and a castle, which is a hotel today. You can hike, bike or paddle to remote Sorbian villages (the Sorbs are a Slavic minority). Very relaxing area.
It takes ~40min to the airport, and the Autobahn is not as busy as the other ones.

Here is a nice blog post about it:
http://www.annees-de-pelerinage.com/visit-spreewald-best-day-trip-from-berlin/

Magdeburg is an interesting city, totally not visited by North Americans. In 2009 I stayed there two nights, the Zentrum has interesting buildings and displays, all the more so if you're into science. It's also another city where you can walk across the Elbe just as you can do in Dresden and Lutherstadt Wittenberg.

Thanks. Those are good suggestions and I liked the article you linked.