After Nagasaki, and before the Japanese capitulation, the plan was to drop a third bomb, which was then on its way. Paul Tibbets was to fly that mission as he recalled in this 2002 interview with the Guardian
https://www.theguardian.com/world/2002/aug/06/nuclear.japan Thats one source. Yet in other sources that I have read vary both in the identity of the target and even if there, in fact, was a third mission planned at all?
Has it been clarified with any certainty? Were any attacks subsequent to third one planned? What were the targets and were the dates and crews assigned?
There was never any confirmed target for the third mission since it could not have begun until the third core was delivered to Tinian and assembly of the weapon had begun. That would have put limits on the possibilities due to weather. The third bomb would have been ready to ship to Tinian on August 12 or 13th, and thus ready for use by August 17th or 18th or so. Truman halted the shipment and use of further bombs on August 10th.
That being said, we have several possibilities that various historical actors either voiced at the time or after the fact. These include:
Kokura or Niigata, the two remaining targets on the initial target list that were un-bombed (Kokura of course was the primary target for the second bomb, and Nagasaki was used because of weather/cloud/smoke issues). In theory this would have been the only option available without getting approval "from the top" since they were "pre-authorized" by the July 25 strike order.
General Spaatz pushed LeMay to get Tokyo cleared as a target on August 9th. On August 10th, General Groves recommended to General Arnold that Tokyo be approved as one of the pre-authorized targets. It is not clear whether it was authorized or not.
On August 14th, prior to receiving notice of Japanese surrender, Truman told the British ambassador to the US that "sadly he had no alternative but to order an atomic bomb to be dropped on Tokyo." Is that a serious thing he would have done, and would Tokyo have been the true target (was he even meaning it specifically and not just as a metonymic?), and would his advisors have pushed him to do otherwise, etc.? We don't know, because the Japanese surrendered shortly after that and so nothing came of that.
I seem to recall seeing at least one other General who had a "list" of possible targets but I am not finding it right now (and need to run to teach in a moment; I'll try to remember later — I have a cold and it is making my memory poorer than usual on these things). The short answer, though, as you can see, is that there were some trends towards Tokyo (which doesn't really answer the question in detail since Tokyo is very large relative to the size of an atomic bomb, unlike Hiroshima, so there would be further thought that would have to go into it), but it is totally unclear whether that would have withstood scrutiny. There was a separate group, notably General Marshall, who thought that the further atomic bombs ought to be saved up and only used once several were ready to use, in support of an invasion attack.
Missed in the OP, Tibbets states to the Guardian that Le May never told him what the target was, did Le May ever indicate perhaps in memoirs or in declassified documents?