They get a certain number of visits, right? I believe it's 30. I've heard that teams meet with players that they doubt will be available via draft just to learn about them for later in their careers. One question they say is also asked is "Who should we be interested in that you've either played with or against?" in one form or another. You need to get as much information as possible in your allotted visits.

I have also heard that teams don't even visit with players that they already have decided to target. It makes sense.