Regardless of which way you decide, @Time2Shine, I wouldn’t worry about the psychological angle of “scheduling visits before being admitted will be perceived as a demonstrable sign my son isn’t sure he wants to attend each school”. I think colleges expect prospective students to want to visit before committing so I don’t think they would read an unintended meaning into it.
Are you flying or driving? Flight costs could go up but I’ve found that for many flights these days you can still get good deals several weeks out and booking early isn’t necessarily a savings. Depends on routes and seasonality, though.
I guess it depends on the schools and the likelihood of your child getting a yes. Are these far reaches where acceptance rates are dismal for most or would be a longer shot or more matches for your child?
Another thing I’d through out there is that you never know what kind of incentives are tossed your way with an acceptance. I don’t know how common it is but surprisingly several schools offered to fly my kid out for accepted student days (and in two cases one or both parents as well) as well as pay for other trip related costs. If we had already planned and paid for it, we wouldn’t have benefitted from that cost savings.