Don't go to Scandinavia. Too expensive, not enough to see. Iceland is expensive too. The main attraction of those places is the countryside. You got woods and wide landscapes in the US too.
Don't go to Amsterdam, it's a boring filthy tourist trap, filled with drunk teenage tourists who wanna smoke pot. I wouldn't go to Brussels either. I would also skip eastern countries (Poland, Romania, Slovakia, ex-Yugoslavia, etc).
I'd stay in the southern countries if I were you. Better weather. (It's not fun if you are in London and Brussels, and you get 7 days of rain).
You got only 7 days, 10 days maybe. Don't try to travel too much. Even if you do a schedule of 1 day in a city, 1 day travel, 1 day in a city, 1 day travel, you get to see only 3 cities. You might think Europe is small, but it still takes a day to travel by plane from Madrid to Rome.
If I were you, I'd do Madrid and Rome. Or Barcelona and Venice. And for a 3rd city, if you want to see something non-mediterranean, go to Berlin. Berlin a germanic, quite different. A real world city. If you don't wanna go to Berlin, maybe go to Paris then. Or Prague.
Have fun.