Foursquare is interesting as a social experiment but not really something that I want to be a part of especially since I barely use my cell phone. I just don't think it's the smartest idea to broadcast your location at all times.
The Elkhorn Campus Library wasn't in the system but Elkhorn Campus was and did have a Mayor. I wasn't sure that I should claim the library so I'll leave it to someone else.
I lot of locations that are frequent are in the system, especially restaurants and bookstores. This could be handy to track yourself and see where you spend too much time. I would probably use it more if I owned a smart phone.
I wasn't surprised by the amount of locations in the system because people like to have attention even if it is only online. I seem to have a couple of friends that are always on Foursquare so they're the Mayors of a lot of locations.
One good aspect of it is that you could keep track of how many people check it at the library and what they're saying about it.
Overall an interesting service but not one that I'd be inclined to use.