In your experience, are these cities generally still in Axis hands for some time after the atomic bombs are dropped?
Absolutely, especially when the AI has control of the Allies. The AI's grand strategy in the Pacific Theater, as well as some tactical operations, lacks cohesiveness, allowing the Japanese to easily continue the war into 1946 and sometimes 1947.
On a side note, I've had discussions with a couple of Japanese friends about the Hiroshima bombing and the necessity (or lack thereof) of also bombing Nagasaki, to which I've usually pointed to the usual suspects: U.S. reluctance to continue the war on Japanese soil (ie., body count) and the requirement/interest in an unconditional surrender as quickly as possible. One response I heard on a couple of occasions (mind you, this is passed down from somebody who knew somebody in the Japanese government, unofficially of course) is that the Japanese moved hastily to capitulation, partly out of fear that after Hiroshima and Nagasaki, Tokyo would be next. Interesting perspective . . .