If I had a month I'd spend 4 or 5 days each in 4 or 5 of the following cities: London, Amsterdam, Paris (not the easiest place to connect with other young people, but a must-see), Barcelona, Rome, Prague, Berlin (not beautiful in the usual old European sense, but interesting people and an interesting vibe).
If you are converting dollars into euros you will find everything to be expensive. With a little planning and research into pensions and hostels you can keep it down though. Beer and wine at the local supermarket are still cheap.
Bon Voyage.
Tony
