Spain is a great country. I have been to Madrid and Barcelona. Although a lot of people like Barcelone better, I found Madrid more lovely. Try both of them.
Paris - Subway will help you get around a lot. Tons of history. Definitely a must. Don't skip it.
London - Duh.
Amsterdam - A definite must do. Head to Red Light District. You will thank me later
Brussels - Capital city of European Union. Try to see Mannequin Pis. The pissing kid.
Trains are abundant. If you are not looking for luxury, they will help you travel around. There are also cheap buses. Try Eurolines. They don't have the best buses and they stop a lot but it is a good cheap alternative.
If you would like to fly, try Ryanair and easyJet. They are good, cheap flight alternatives.
Ask specific questions and I will try to answer as a regular Euro visitor.