Oh my god we have the SAME thing going on. It's quite amazing!
I was invited to the visit weekend at one school with the same profile. Great great great research topic, awesome advisor, very famous advisor actually. But the school is not ranked as high as i wished it was (comparing with my other acceptances, this school is in the mid thirties, while the others are in the top 15).
So I visited the campus two weeks ago in a similar way you'll do next week. I asked millions of questions to make sure i liked the institution, students, professors, etc. questions ranged from: "do you like working/studying here?" to more research/funcing/course-load related.
In the end of my visit I was really in love with that school and I might choose them (top 35) over the other schools I got in (top 10). The thing that gets me a little iffy is that this school is not located in my dream city, but oh well, we can't have everything we want right?!
Enjoy the visit and pay attention if you can see yourself living and studying there. Take a feel for the overall atmosphere, how friendly they seem to be, and how the other phd students are (afterall they might become your next group of friends). And more than that, ask away! Ask as many questions you can.
This type of visit is more for you to get a feel of the area, so make sure to do that.
And congrats! Never thought someone would be in the same shoes I am :-)