If he is actually personally determined to play in college, then he should definitely have his top 3-5 schools in mind by the end of May, so that he can try to get them to come to his summer games to see him play. Actually I prefer that players get this done by January, but while that's the optimum, there is some lattitude here.
I do think that all you can do as a parent is make the point that it's not enough to SAY he wants to play in college. Deeds, not words, reveal the reality. So either he does what the process requires of him, or a year from now, he doesn't get to bitch and moan if it doesn't go his way. If he has the desire, he'll do what's required, all on his own. If he doesn't do the work, then that means he didn't really want it after all, no matter what words he may speak.
I would add that a big problem we have is with players who keep playing travel ball etc., not really appreciating what the collegiate baseball experience is all about, for no reason other than it seemed to be what everyone else was doing or what other people expected of them. A very high percentage of these guys get to college and end up getting cut or quitting.
So my principal advice to you is to let your son find out right now whether he wants it or not. Stop nagging him. For good or for ill, it's his future and it's up to him to choose his path. Tell him, once but only once, that he knows what's required if he truly wants to play in college, so either he does what's required or he should expect not to get to play. Then sit back, say nothing more, and see what his real preferences are, once they reveal themselves.