I will be visiting New York this summer, and I have a few questions . I will probably be visiting university of Rochester, brown, and Cornell. Since I heard showing interest in colleges is important I will go on official visits. But to show more interest what kind of things should I do, what kind of questions should I ask
Interest is not important to all colleges. Google the common data set for each school to get that information. Visiting is a good start though. Nobody will keep track of what/if any questions you ask. In the fall you can request interviews for schools that do interview candidates.
We met with professors/directors of the programs my children were interested in. I simply looked up the department and contacted them to set up meetings during our visits. Then my children were able to discuss their visits with the professors in their apps. I think it helped a lot but as mentioned, it is more important a factor at some schools over others.
Typically the only way meeting with a prof or director of a department helps is in the “Why College X?” essay. One of my kids did that a couple of times, the rest of the time they just sat in on a class where possible. Generally, more time on campus, and more interaction with students and staff gives you more information for those essays.
Google “Common Data Set” and the college name, and in most cases you will find a document that includes (along with tons of other great info) an assessment of what is important in admissions.