I think you have to go Paris and Amsterdam. They're two of the more unique cities in the world, they're both awesome, and they're a short train ride away from each other.
After Paris and Amsterdam, I'd suggest Rome, London or Prague. If its London or Rome, I don't think you'd have time for anywhere else, but Prague is compact enough that you can get by with only 3 nights there and then fit in another 3 nights in either Berlin (if you're into WWII/Cold War history) or Budapest.
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