The ball is in your court in terms of his appeal to other schools. Do the campus visit, say that you're very interested in the offer and would like to talk it over with family and ask how long he has to decide. If they ask if you plan on going on any other visits just say yes as you want to compare campuses and different types of universities (big, small, rural, urban, etc). They should understand and at the very least give you a week to decide.
In the meantime he needs to be emailing/texting/calling all other schools he is interested in or has been in contact with and say that a school he is interested in has made him a nice offer and he is considering accepting it. The schools will put up or shut up and you will know how interested they are/were. If a Big 12 coach calls that means he wants your son. They don't call guys to make friends so don't shrug interest off, they're not doing it for the sake of doing it. Your coach can help here and make some phone calls on your sons behalf. If none bring you out for a visit or make an offer, you should probably not hold out any longer.
You're in a good spot. Don't let the school rush you and don't take forever to decide. If this school is the only offering well that may also be a sign that he needs to take it while it's still there. A teammate of ours went on a campus visit to a mid major D1 to tour the campus and facilities. They asked where his other offers were from. All D3s and a perennial bottom feeder D1. They never ended up offering, figuring if no other schools of that caliber were interested, they shouldn't be either. He ended up committing to a local D3 with a sub .500 record. Knowing your pond and your value is important, the same way you don't want to jump at the first good offer, you don't want to pass up the only good offer.