Hans Li, you are welcome.
I googled you a map of germany:
Google-Ergebnis f�r http://www.sitesatlas.com/Maps/Maps/511.gif
Here you can check up on what places you urgently want to see and where they are and then decide which city is best for you to stay in.
Because from here I can only guess what you want and what would be perfect for you.

Feel free to ask me about the locations you think interesting, I might not know all the cities though.
One can drive from hamburg to munich in one day, will take some time but it's possible.
From cologne to berlin it might be about 7 to 9 hours, depending on how the traffic is and how fast you drive.
Dunno about how long it takes with a train.
Now that you mentioned you want to see the car factories cologne is not the best choice for you.
You might want to aim more south.