Not so much where did they go, but what these men do in the down time? Were they sent to the pacific? Were their campaigns in Europe that were accessible? Did they patrol the African desert?
Just as a hint, Rome fell to the Americans just two days before D-Day.
Well, the ones that participated both in the North Africa Campaign as well as the invasion of Normandy such as the 1st Infantry Division "the Big Red One," initially took part in the invasion of Sicily almost immediately after the North Africa Campaign and where then shipped to England afterwards where they remained training until the Normandy invasion.
If I remember correctly, most of the units from Africa and Sicily continued into the invasion of Italy and many of the U.S units that took part in the invasion of Normandy were as far as I know newly reactivated such as the 4th Infantry Division, 29th Infantry Division, 90th Infantry Division, 2nd Ranger Battalion and 5th Ranger Battalion.
So basically unless I am wrong, most of the US soldiers from the Normandy landings were either (mostly) fresh reinforcements or veterans of primarily the invasion of Sicily and to some extent the invasion of Italy as well as the North Africa Campaign.