The Forbidden City in Beijing is probably up there. I never seem to get tired of the place.
Agreed. For me, DC will always, always top the list of world cities. As with any city, parts can be drab (L’Enfant Plaza, I’m looking at you!) - but there is extraordinary beauty here. The Library of Congress, the National Cathedral, the Tidal Basin - but more than that, there is extraordinary joy to be found in the District. Our art galleries, music scene, theaters, restaurants - I’ll put them all up against anything in the world, even NYC. (New York is bigger, I’ll grant, but we’ve got plenty of quality.)
I’ve been having kind of a cruddy couple of weeks, and yesterday I got sick of feeling sorry for myself, went out for a walk. Around the Tidal Basin - honestly, I don’t think there’s a better cure for self-pity than such a walk on a warm fall day.
As for other great cities:
2.) Monteal, in summer: Art! Poutine! Architecture! And, the last time I went, they were hosting Worldcon!
3.) San Francisco, any time: I defy you not to love a city whose idea of sound public transit is “You see that platform barreling down a hill in the middle of rush-hour traffic? Yah, you’re going to cling to the running board on the outside of that thing, and try not to lose your grip.”
“Well, wait, what happens if I do lose my grip?”
“Don’t know, but I expect that rather depends upon how you fall, the reflexes of passing motorists, and the quality of your health insurance. Good luck!”
4.) New York City: I wouldn’t want to live here - but I’ve never, ever had a boring visit. 
5.) New Orleans: Even after Katrina, fun beyond all reason.