I could spend a week in Berlin, and I have several times. I love that city.

Hamburg is a 2 hour train ride and I found it a wonderful city. I spent a great weekend there. It was in the summer though.

Cologne was a fun weekend destination.

You could spend the entire 2 weeks in Bavaria if you wanted. Nuremburg, Regensburg, the castles, and Munich and the Alps.

You have lots of choices. German cities are easy to navigate, transit is usually excellent. Its easy to get to cities by train. Flights are cheap and often.

You pretty much cannot go wrong. I travel solo almost exclusively, and I have found Germans amongst the most affable people to meet and get to know as a single traveler. Its become one of my favorite countries to travel in.