I’ll just rank the European cities that I’ve spent more than a day in, with a blurb about each.
#1:  London.  Like others have said, it’s just spectacular.  Great tourist attractions, extraordinarily cosmopolitan feel, relatively clean and everything works.
#2:  Rome:  Incredibly historic- you have something like 2400 years of history in one city, some of it still standing and in use.  Plus, it’s a modern big city, and has all that comes with that.
#3:  Prague:  Maybe not as historic as Rome, or as cosmopolitan or well organized as London, but really beautiful, with extremely friendly people, and a really nice feel to it.  Terrific beer and good food as well!  Kind of dirty though.
#4:  Edinburgh:  Kind of like Prague, but full of Scots, who I happen to really like and get along with.
#5:  Budapest:  It had a strange feel to it, but the people were good, and the place has some really interesting things.  Plus, the Hungarian people and language are different from the rest of Europe, so it’s interesting for that as well.  It is a beautiful city as well, but has that Eastern European/Paris/Brussels grunge to it though.
#6:  Florence:  Really touristy, but very pretty, and with good food and some of the world’s best art.
#7:  Oxford:  Did a study abroad here.  Fun place, very historical and worth seeing if you’re in the UK.
#7:  Amsterdam:  I didn’t spend long enough there to really get a great feel for the place, but what I did see, I liked a lot.  Very friendly, very clean, very well run (like the Netherlands in general).  I didn’t feel like some gypsies would pickpocket me in Amsterdam, unlike most other European cities.
#8:  Paris:  Astoundingly pretty city, but filthy dirty, and full of Parisians, who seem to be their own brand of rude, unlike any other.  Great tourist attractions and stellar food though.
#9:  Brussels:  Good food and beer, and that’s about it.
Places I’ve day-tripped to:
Bruges:  Really touristy and crowded (at least when I was there), but still a fun city.
Ghent:  Less touristy than Bruges, but still has interesting things to see.
Delft:  Neat stuff to see, nice people, etc…
Utrecht:  Neat stuff, nice folks, but not much in the way of touristy stuff.
York:  Pretty cool- the Minster and the Shambles are definitely neat to see.