At the risk of starting a "He said, She said" discussion, my favourite major European cities, in order (YMMV): Prague (by far), Paris, Berlin, London, Venice, Innsbruck, Bratislava, Florence, Lisbon, Barcelona, Copenhagen, then all the others. You can do countries, or you can do cities, but unless you're there for a while it's hard to do both. I lived in Europe for a half-dozen plus years, so I had the chance to do a bit of both. As for suggestions, it would depend on which time of year you're traveling, and my recommendations would be based on weather and timing to avoid the tourist crowds.