We don't really know much about how FDR thought about the use of the bomb. He kept no diary or notes and talked to almost nobody about it (and wrote no memoir). We barely know what he even thought about making it, except he obviously approved the plans to do so. FDR is very tricky for historians because his documentary habits, and penchant for personal (as well as official) secrecy, leave a lot to be desired. He is a hard historical figure to get inside the head of. (Truman, by contrast, left much more of a record.)

There are literally only two instances in the historical record where FDR himself made a reference to using the bomb. The first is what is known as the Hyde Park Hyde Park Aide-Memoire, an agreement between FDR and Churchill from September 1944. Among other things, it contained this line:

when a 'bomb' is finally available, it might perhaps, after mature consideration, be used against the Japanese, who should be warned that this bombardment will be repeated until they surrender.

Which indicates that he considered a possibility, but it is not a commitment.

More interesting, in my mind, is an account from Leslie Groves, the military head of the atomic bomb project, in which he recounted that Roosevelt did ask him about using one on Germany in December 1944. The bomb wasn't ready, though, so obviously that couldn't take place.

The latter is more interesting to me primarily because it is not a hypothetical question about using the weapon, but an apparent desire to use it in the near term, indicating (unlike the Hyde Park Aide-Memoire) that the idea of use on a city did appeal to Roosevelt.

But literally, those are the only two sources we have on FDR's thoughts on use of the bomb. Everything else is just interpretation or guesswork.