Upvote:2
United States nationals can enter the Schengen Area for stays of up to 90 days and travel freely within the area, as long as their total time spent in all Schengen countries does not exceed 90 days in any 180-day period.
So your son will not need a visa at all.
If he leaves the Schengen Area (such as to go to the United Kingdom) whether he needs a visa will depend on the rules of the country he's going to, of course. However, there should not be any trouble getting back into the Schengen area -- on the contrary, the 90-day limit will be extended by the number of days he spends outside Schengen. Be sure to get appropriate exit and entry stamps when crossing the external borders.