I completely agree with this, exceeeeept, I didn't visit any of my programs until my admission status was known. Once you're admitted, most schools will pay for your travel costs to visit. Plus, it's a strain on faculty to dedicate their time to arrange your visit if you might not even apply, let alone be accepted into the program. Much better for you and the faculty to wait til you get that acceptance.
I also wanted to stress to make sure the professors you're interested in aren't retiring anytime soon.
#1 thing is the fit -- are your interests a good match for the program? Are there faculty outside of the department that are also good fits for your interests that could be on your dissertation committee? Will your research be supported there? Are there strong fits for mentors who have the time to dedicate to you?
Good luck!