A little background:
-I'm traveling to Europe on 5/1/13 and won't be coming back until 5/24/13.
-I've been to Eruope twice before, once on a study abroad program to Madrid in college and once with an ex-girlfriend. This will be my first time traveling abroad by myself.
-In my travels to Europe before, I've seen most of the major cities/attractions in Spain, France, Italy, and England.
I'm flying into Manchester on 5/1 and I have to be in Liverpool on 5/19 for an LFC match (I'm a fanatic). Other than that, my travel plans are wide open. I was planning on checking out Amsterdam, Berlin, and Munich as those are places I've never been before. I also want to spend a few days in Paris and Edinburgh since I have friends in those places with whom I would like to visit.
So what I'm asking for are your opinions on where I should go and what I should see. If you had 3 weeks to trek around Europe, what places would be on your must-see list? And I'd prefer to see new places that I didn't note above.
Thanks in advance!