Truman didn't actually make a decision to use the atomic bombs (that is, the portrayal of him agonizing over authorizing its use is incorrect; he essentially deferred to military leadership on the topic, and the train was down the tracks). Here is a link from /u/restricteddata's recent AMA:

https://www.reddit.com/r/AskHistorians/comments/3e76ig/ama_the_manhattan_project/ctchcri

That comment is short, but it links to /u/restricteddata's blog, in which he elaborates on the targeting decisions.