Have you considered the upstate NY schools? Not on your list of states, but Buffalo is less than 2 hrs from the Ohio border, and SUNY Buff is an excellent engineering school that’s quite affordable for OOS students. They also offer a minor in Chinese. Another hour or so past Buffalo, Rochester has both URochester (which has a very large population of Asian international students, and excellent course offerings in Asian languages & cultures, in addition to very strong STEM - also a great school for an orchestra kid) and RIT.
Lots of excellent options in Ohio, though, and the other states you mentioned. Cincinnati for a strong co-op focus (they basically invented co-op education). OSU, Purdue, etc. as others have enumerated already.
If participating in music is important, tOSU has a great music school that is more non-major-friendly than most. Strong Chinese program too, with extensive undergrad offerings and a grad-level language flagship program. Seems to me that tOSU has everything he’s looking for, for a great in-state price.
OTOH, if a large public doesn’t appeal and a small, hands-on school would be better, look at Rose-Hulman in IN. No Mandarin at RHIT though.