So Hamburg, what everyone keeps forgetting is how... Um... Seedy the town is. The Davidwache, where the hookers are, is interesting. The other street, I forget the name, is where all the sex shows are.
I've actually driven all that way to see the museum but didn't get my tickets in time so didn't get to see it. I'll have to go back in a few months.
There are many things to see in Hamburg but that extra drive might not be worth it.
Your trip is mostly Autobahn, I'd suggest turning on the scenic route, Europe in the spring is amazing. So much to do and see. Like on your trip from Frankfurt to Heidelberg you pass Frankenstein Castle. Just so much here to do and see, don't speed by it all.
The Ultimate Driving Machine drives me, what drives you?