That’s a pretty unusual background for a high schooler. Classical languages are typically taught more rigorously and at a faster pace in college than in high school, but nevertheless he should have a pretty good reading knowledge of Greek and Latin by the end of next year. (Put another way, he should be ready to handle Cicero, Vergil, Horace, Catullus, etc. in Latin. In Greek, he should have already read some Plato and will hopefully be prepared to tackle Herodotus or Euripides in Greek.)
For this reason, he should scope out the classics offerings of any school VERY carefully. I can already warn you that he’ll be very dissatisfied with the classics offerings of most LACs and quite a few universities. They simply won’t offer enough upper-level courses on a regular basis. You can find dozens or even hundreds of good programs in biology, history, or English, but the quality of classics programs drops off noticeably outside the dozen or so best programs and then more sharply after another dozen or so programs. This is admittedly not as big a concern for a pre-med as for an aspiring classicist, but it’s still something to consider. I would look for programs that offer at least a MA program in classics, as he should be moving into graduate courses in a year or two.
Tulane has a reasonably good classics program and offers great merit aid.
http://www.tulane.edu/~classics/
Boston U is another possibility, especially if he can get his test scores up.
Several of the southern schools have good classics programs and offer merit scholarships to the best OOS applicants (UGA, UF, and FSU in particular).
http://www.classics.uga.edu
http://classics.ufl.edu
http://classics.fsu.edu
Arizona has a very strong classics program and offers decent merit aid as well.
Villanova and U Dallas are other options.
Among LACs, Oberlin and Trinity (TX) come to mind for classics and merit aid.