I remember reading that Vegas gets somewhere around 37 million visitors a year, surpassing Mecca as the most visited place on earth. Try googling, Vegas Mecca Most Visited.
Agree that it's difficult to define "visit" You can't really rely on airplane or rail statistics because man of those travelers are coming "home" and thus not "visiting". And, it would be very difficult to estimate the number of visitors arriving at a place via automobile or on foot.
I imagine that the best you can do is figure out the number of hotel rooms, or any type of temporary lodging for that matter (campgrounds, hostels, B&Bs, whatever), get some numbers for occupancy rates, and use that as a basis for determining visitors. Of course, this precludes daytrippers.