A few favourites of mine:
New Orleans - for its unique culture, best food anywhere, great music, and most of all the friendliness & southern hospitality of its people.
Chicago - if I was to move to the USA I would live there. Big city diversity with a more relaxed midwestern pace than the US cities on the coasts. I don't know about winters though.....
Venice - because it is so unique. Couldn't live there but to visit, the maze of misty little lanes & canals is just magical, there's nowhere like it.
Detroit - yep really. Don't ask why but it fascinates me. I have been twice and going back next month.... I find its heart, grittiness, the fact that there is so much pride in a place that struggles so much, the optimism for a rebirth, its Motown history, its love for its sports teams, and the strange beauty of something once so grand being in such a state of disrepair to be really compelling.
San Francisco - natural beauty of its location. The fact that you can walk to certain street corners and see amazing views in every direction.
It's a pretty US centric list, that's where I have done most of my travelling (a couple of big road trips through about 30 states and another coming up in February-March) but I've also been to Europe a couple of times and while I find Europe very interesting and really liked cities such as Venice, Nuremburg, Amsterdam and Athens, I tend to be more drawn to the US cities, particularly in the south & midwest.