New York. Great place, felt right at home but... it's in America. Even with Obamacare...
London, England. Great history, but the crowds are just horrendous.
I agree entirely about Central London, but it gets better in Zone 2. My home town.
Chicago. Shopping the Miracle Mile, visiting the museums, maybe a walk on the Navy Pier, a lot of things to do there. But after a couple of days my patience wears thin dealing with the traffic, the panhandlers, and the crowding, I retreat back to my small midwestern town and enjoy the peace and quiet.
I don't think there's many places.... I realised that the things I've loved most about places I've lived are the things an outsider wouldn't know - the right cafés, the pretty places to walk, when to do what, how to talk with local people, etc.