School visits can make a difference - but not for the reasons you think.
The visits aren't for the adcom's benefit. They are for YOUR benefit. Regardless of whether adcoms track visits or not, it's not about "oh, Aboo visited our school. That's a plus. Check." They're not doing a Best Buy product comparison grid with applicants or anything when it comes to decision-making.
You visit the school to get a better handle on what the school environment is really like. You sit in on class. You speak to current students outside of class. You spend the entire day on campus. Through that experience, you should be able to develop a better understanding for how the school could be a great fit for your individual needs and circumstances. It helps you personalize the "why school XYZ?" question in the essays. It's not necessary to visit the school, but it certainly helps.
For example, HBS doesn't track visits, but it's still helpful to go visit the school if you're interested in applying there because it'll give you a far better idea of what you're getting into which can help you in crafting your application (even if HBS doesn't even ask the "why MBA?" question) and will help you figure out how you will fit into HBS should you actually get an interview.
Also, if you visit in June you'll be on an empty campus. Remember that school is in session from Sept - Apr (May is final exam/project week and students begin to check out).
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