Dear yankexpat and Chris,
Campus visits are a great way for you to learn about a program an determine if it is a good cultural match for you. Likewise, it gives the school a better idea of who you are as an applicant and puts a face to your application. Good questions to ask are those that will gain you insight into what the program is looking for in its applicants (beyond the obvious) and what traits are valued more than others. For example, almost all programs stress the importance of teamwork. You can ask more specific questions around teamwork opportunities: what percentage of your grade is based on teamwork? are teams assigned or do you pick? what other opportunities do you have outside of coursework to be on a team with your classmates (i.e., case competitions, club leadership, etc.)?
Schools do not view applicants more positively for visiting nor do they penalize applicants who do not visit. Schools always like for applicants to visit and attend class because it shows that 1) you are genuinely interested in the program and 2) you are doing your due diligence to make sure the program is a good fit for you. If you cannot visit due to personal situations and/or a geographic obstacle, then you might consider adding a brief paragraph in the additional information/optional essay section explaining why you are unable to visit and what you have done to learn about the program. Likewise, if you do visit a campus, be sure to make the best impression as you are being watched and folks will give the admissions office feedback on you.
Best of luck,
Lisa