FDR would be dead by year's end anyways unless you have a much earlier POD which butterflies some of his helath issues. Still drops the bomb, probably lets Dugout Doug run Japan as well.
I'd say the most he could have done in the literally most optimistic scenario possible without his Warm Springs stroke was to finish out the rest of his term, an earlier PoD would be interesting though, FDR never really slipped in terms of
intelligence (i.e. something like the onset of senility or dementia) but he tended to get worn-out earlier, at wartime conferences and things of that nature that can prove a handicap when up against (slightly) more energetic leaders with ambitions of their own.
Almost anyone in that situation would have dropped the bomb, nobody is going to touch Operation Downfall with a 50-foot pole and the massive military mobilization was becoming enough of a drain on the economy that a campaign of blockades and bombings (which would have also killed more Japanese than the a-bombs) was also unpalatable.
Germany winds up pretty much like OTL, we would have had the same harsh treatment of the Germans in terms of being stingy with food and medicine supplies in the immediate postwar environment the same way it was with Truman as FDR was very much of the persuasion that the Germans needed to
pay for what it did. However we'd probably see about the same postwar plan as we did historically, Roosevelt would drop his own plan and the Morgenthau Plan is never going to see the light of day.
FDR's Soviet policy might be slightly more oriented towards rapprochement, but FDR will almost certainly see that Stalin has some ulterior motives that don't always have Allied interests at heart. FDR is a man who admires the Soviet system, but ultimately he is a wise one quite capable of seeing such things.
Domestically we might see FDR's magic touch give us some things from his Second Bill of Rights... healthcare might wind up becoming a much more ubiquitous thing for all segments of American society.