I like Kobe very much. It feels like a very 'international' place downtown, but it's not overly large. Once you leave downtown, things can get very local. It's also also just a hop away from Osaka and two from Kyoto, which makes it a day trip away from a good chunk of Japanese culture.

I'm afraid I can't compare it much with other cities, as I've spent much more time in Kobe than anywhere else, and it's only been a few months so far.