I'd advise your son get to campus and take summer courses. There isn't much he's going to gain by playing another couple of tournaments but there are a number of very good reasons to get to campus early.
1. Face time in the training room. The coaches won't be there much but they do want to hear from the trainers about your son's work ethic. A good chance to make a great impression.
2 Early credits. They'll have your son take some easy credit classes to boost his GPA and reduce the number of credit hours he'll need to take in the fall and spring. Don't let anyone kid you about the NCAA limits on baseball related activity. It's a 60 hour commitment so taking 12-13 credit hours during the first semesters is huge until they get accustomed to time management and no sleep.
3. It's fun. Get to know your teammates and let go of the travel team. It's time. The summer is fun for these guys. They'll soon realize a lot of things that aren't in the recruiting brochures which aren't a lot of fun such as hell weeks in the fall. No sense in that being your first experience.