This has been answered on here several times before — there's a fairly long discussion here and here. The original targets chosen by the military were Kyoto, Hiroshima, Kokura, and Niigata, in that order of priority. Kyoto was removed from the list by the Secretary of War (a whole story in and of itself), and in order to have another backup target for the Hiroshima and Kokura missions, Nagasaki was added at basically the last minute to the list. The original plan was Hiroshima and Kokura as the first two targets, but the Kokura mission went wrong for various reasons and the back-up target, Nagasaki, was used instead. The linked-to post discusses in some detail why they were attracted to some of these targets over others, and the process used.

As for why not Tokyo or Okinawa: they wanted the first use of the bomb to be "sufficiently spectacular" to force the Japanese (and the rest of the world) to take notice of the new destructive force. The scientists, military planners, and civilians involved in the planning for the bombs thought that bombing an essentially un-bombed city would showcase the power of the bomb most of all. Tokyo had been extensively bombed by that point in the war, and so while it might have had political importance (and a large death toll, as many people were still living there), it was not considered a candidate for the first use of the bomb. (Whether it would have been used as a target for a third bomb is possible, but unclear.) As for Okinawa, the US took the island before the atomic bombs were ready to be used. So even if a "tactical" use of the bomb had been contemplated for the first use (it was not), it would never have been a target just for the timing reasons (the US would be bombing itself). Lest one wonder, why didn't they delay Okinawa until they had the bomb? — the island-hopping campaign and the bomb development were totally separate and unconnected. They also were not sure whether the bomb would actually work, nor how impressive it would be, until they had it, and they weren't 100% sure when they would have it, either. So they didn't make any planning based on it until it was in hand.