One common trope in discussions about Operation Downfall is a guerilla war waged by fanatical IJA soldiers against the US occupation. How long would such an insurgency last?
OTL guerillas fought the Soviet occupation in Eastern Europe for years after WW2, but most of the fighting died down by the early 1950s, with small pockets holding out longer. Compared to Eastern Europe, the mountainous terrain of Japan seems friendlier to guerillas, and the fighters would probably be far more fanatical than their Baltic or Ukrainian counterparts. But the insurgents are not going to have a reliable source of weapons or ammunition. They'll be limited to what they stockpiled from before the war and whatever they can steal from the Americans. They won't be able to import anything (the US navy would prevent that) nor would anyone be all that willing to supply them. Most importantly the US controls the food supply, leaving the guerillas only what they can buy or steal from the Japanese people. There's also the issue of war weariness - how many Japanese would still be willing to fight after a horrendously destructive invasion of their country? They might not like the Americans, but now that the war is over, how many would want to throw away their lives in a lost cause?
So I think the insurgency would mostly be defeated by some time in the 1950s, with some fanatical holdouts lasting longer. But I think by and large most Japanese would reconcile themselves to the new order, and try to go on with their lives.