Reality check (private colleges & merit aid) & whether it's worth it to research/apply

Thanks to all for your speedy & informative replies. I’ll try to quickly respond to each here:

@STEM - Thanks for the specific suggestions. I’ll ask son to evaluate & run the NPC/check into scholarships.
@tavern - That’s a good point… I think as he starts to get more specific (hopefully), we might select a few “reaches” based on location & promising merit aid & be open to see what happens.
@Eeyore…I think it’s going to be hard to beat either tOSU or Miami for costs, as I suspect ds will get strong merit aid from each. We’ve planned for some budget creep (our upper limit is $35K/year, but we’re telling him to select for $32.5/yr now, since it will creep…although, again, that’s an argument for a state school, since some (all?) of them have the tuition freeze option for incoming freshmen.
@chaphill. Good point. He has had a slight preference for smaller schools, just because he does better in a more connected environment (emotionally). However, as you note, some large schools have “small school” options/programs within them, and that might be ideal for him. If he decides to do pre-med, professor access will be important. And I have to edit my OP - he actually hasn’t taken the SAT, the listed score is his PSAT scrore. His selection index was 213; not high enough in OH.