For those of us who have only limited budget. You may wonder why visit a school before you are admitted. Well, there are at least two reasons.
1)Some schools are "show me love" schools. They will treat those visited differently than those who didn't. Wash U is a well known example. On the other hand, most of top school really do not care if you visited or not. I think P does not even keep an record of daily tours.
2)Most of the schools will request a "why xxxxx" essay on top of the common app essay. A visit on campus COULD help the child to write something if they have seen it with their own eyes.
Just be aware that some schools require a reservation for school tour and not all the school offer free overnight to every visitor. They typically only do overnight for admitted students or some special students they really really want.
On most of the tours, they will only show you the good part of the school. Few will show you the inside of any dorm.
So, if you have some budget and your children are interested in some of those "show me love" schools, go visit. Otherwise, do the admitted student days will have more value. Again, some schools will offer free airfares etc to get their top admitted students to stay a couple of days. The student gets a lot more attention during those visits.