In München:

• Deutsches Museum: so much technical stuff there, including stuff about engines. They even talk about direct injection, go figure.
• Englischer Garten: Try running that. Bigger than Central Park.
• Enjoy lunch (Mittagsessen) at a Biergarten, at your leisurely pace.
• BMW Welt- self-explanatory.

muenchen.de - Munich Germany Bavaria bavarian german
For more info. English can be selected at top left hand corner.

In Berlin:

• Brandenburger Tor and Friedrichstraße- Lot of history related to these two.
• Checkpoint Charlie- it was just the 20th anniversary of the fall of the Berlin Wall.
• Reichstag- The German equivalent of Congress.
• Make note of the differences between former East and West Germany. They're still there (such as the pedestrian signals, or Ampelmännchen)

Berlin is a more bustling metropolis and a more "hip" place to be, but it also has a lot of history especially of that within relatively modern times. I like München better but that's a personal preference. A lot of Berliners find München to be too stuffy and haughty; there's the saying: "Berlin: Arm aber sexy" (poor but sexy)

I know you aren't going to listen to me, but I'd avoid driving in the urban centres whenever possible. Petrol and parking are pricey, and Germans don't like lost drivers. No right turn on red!

Wichtig! (Important) If you drive your rental into central Berlin or München, you must have an Emissions sticker on the windshield for the Umweltzone (environmental zone). It's likely that your car will have it, but it's cool to make sure.