The town of Schwerin also has a charming historic center. There's a castle on a peninsula in a small man-made lake in the middle of town, surrounded by gardens. I don't know how much that would appeal to young males, but I liked it.
I'm sure there are other interesting destinations up that way, but I didn't make it farther than Schwerin.
Actually, my top recommendation would be that you double up on lodgings for a few nights and spend some time in Berlin. The hotels are remarkably moderate in price for a capital city, and there is tons-tons-tons to do there. It doesn't take all that long to get to Berlin by train from Hamburg--about two hours--but I can't imagine making a day-trip to Berlin. I was frustrated with just having six days there. In addition to the magnificent museums (the Pergamon would appeal to just about everyone, I think) and the WW II / Cold War sights, it's a very young, lively city. Unless you get out to Potsdam, I confess that it lacks the gorgeous traditional architecture you can find in a lot of other German cities. Oh--one other thing--Berlin is a great place for non-German food. Which by the middle of your stay you may be craving.
