You may want to glance over current summer rosters, just to get a feel for placement: how many freshmen? rising seniors? what colleges do the players attend? are the rosters stacked with SEC, ACC, other? mostly d3?
This may help: http://www.thebaseballcube.com/college/summer/
And there are also smaller leagues not on this list.
All that being said, you go where you coaches send you. Coaches have relationships with summer teams, maybe one per league and they can only send 1 or 2 players. Some players may get several offers, but the coach will ultimately decide. If you don't have a placement by the middle/end of the spring playing season, I would have your player chat with the coach, and be ready to look on your own at that point.
In son's experience: Freshman year, son had a placement by the end of September. He wound up not going due to surgery and rehab during the summer. Sophomore year he knew his placement by the end of August, right when classes began. Junior year they strung him along but he found out it was the cape, and he didn't go due to the draft.
There is a lot of movement in summer teams, at least in the Northwoods League where there are games almost everyday. Players get hurt and go home. Pitchers are on a pitch count and go home. Some find out late that they need to take summer school classes and go home. Some are on a temporary contract and go home or to another league. Some get drafted after play begins and go. Some just.... go home. Some come late because they are still playing the NCAA tournament. Some come late because they are injured, so they come the last half of the summer. By the end of the season, some managers are scrambling to fill in holes. There is a lot of coming and going.
I mention all that because there may be openings during the summer if your son doesn't get placed.
Best advice ever: Make sure your son is in shape and ready to play in the fall.