Whao! Thanks everyone for your replies, I wasn't expecting to get this much of a useful advices, I'm just glad to finally get some suggestion from the ones who know about Germany :)
@Nigel, I have 12 Days including Cologne and I was thinking 3 days would be enough for me to stay there and see what's around. Please says o if you think I might need to spend more time there. I dont mind taking trains but depending on the itinerary I may consider to rent a car.
@Sara, My gf was studying in Munich so she already seen somer parts around there and for that we want visit places where both of us didn't see before. So rather than going down to south heading Munich, I would prefer to stay in the North.
@Russ, I need to return to Cologne since my return flight departs from there back to Istanbul.I'm just concerned about the weather conditions, I am not sure if it would be the best time to see Scenic Valley.
Before I posted in here, I was thinking to hit the places listed below and have a round trip back to Cologne;
Düsseldorf ( My flight lands there at 14:00 so I spend the day there)
Head to Cologne for the night and stay there for 2 more nights. ( a day trip to Aachen maybe)
Bremen
Lübeck (I'm don't know if that makes any sense)
Berlin( 3-4 nights with the day trips around Berlin)
Dresden
Erfurt
MArburg
But again, I dont even know if I have the enough time to see all of them and if it is even logical or not.