So, one thing that needs to change is that the Allied strategy needs to involve the invasion of France before the invasion of Italy. This could lead to a number of interesting things.
So let's say that in Fall 1943 Normandy is selected as the first target for amphibious invasion. The invasion process goes about as well as OTL (the Allies have less experience with amphibious assaults, but the Axis has less experience defending against them, and so on).
OTL, when the invasion of Italy happened, it diverted a lot of German attention from the Eastern Front (pretty much ending the Kursk operation in an instant). An invasion of the Normandy region would likely scare the Germans even more due to increased proximity to Germany itself. As a result, the Soviets have a slightly better several months immediately after this invasion than they did OTL.
As Winter comes to an end in 1944, the Germans launch an offensive in the Ardennes region, hoping to push the Allied forces back and relieve the growing threat against Germany itself. Allied command puts significant resources into utterly crushing this offensive, but at the cost of delaying the invasion of Italy (planned for June 1944) by an additional couple of months. Eventually, Allied planning changes entirely - the strategy simply becomes take Germany out of the war.
Changes to the post-war situation:
- There is no West or East Germany. There is a unified Germany under Allied control exclusively.
- Italy is under control of left-wing partisans answering to the Soviet Union. Greece is in a similar situation.
Eventually, when Tito starts to shift away from Moscow, he has allies in Italy and Greece ready to back him in this maneuver. At this point, changes to the Cold War are so stark that history just sort of butterflies away from there.