Hi Chillinlikeavillain,
I've been to one visit weekend and am going to another in a couple weeks so I'll try to answer your questions based on those experiences. The first one was more of an interview, since they haven't made final decisions yet. The second (upcoming) one I have already been accepted to.
1) Where do you stay?
Usually with current grad students.
2) Do you bring anything? Other than clothes, obv.
I brought a notebook and my questions. I also brought printouts of information (current research, publications, courses taught, etc.) about the profs I'm interested in working with, for reference.
3) Do you go alone?
Yes. You'll likely have a full schedule and, like I mentioned, you'll be staying with a grad student, most likely.
4) What happens at these things?
For me, the two visits are pretty much identical in structure. The first day, you get a general orientation from the Director of Grad Studies and maybe hear from the Chair and others in the department, get a chance to ask questions, and usually get to meet with professors you're interested in working with, as well as current grad students. The second day, there might be tours, a social event with grad students or at a professor's house.
5) Do you pay for it (travel, accom.) or does the school?
This depends entirely on the school and its recruitment budget. One paid entirely for the visit and food. The other is only partially reimburses travel expenses. I've been invited to another tentative visit, for which they'll also likely reimburse at least part.
6) Is there anything you should do to prepare?
Definitely be prepared with questions. It's not a bad thing to have a typed list of questions to ask different people. Be prepared to speak with profs who could potentially be your advisor. Also, be very prepared to articulate your research interests. You will be asked this a lot.
Hope this helps!