@"Leah M B" WUSTL is one of my top two choices (assuming I can muster a competitive LSAT score, I'm battling a huge splitter issue). I would love to hear your thoughts about your visit.
I'd probably vote for a university because it may get a person into a school mindset but some hotels also have very nice conference rooms and I'm sure it varies. Hope you get a chance to visit.
Should you visit the school before applying so you can write a solid why X essay? Do this for each school? Just for your top choice? Just for reach schools?
Agreeing with @"surfy surf". There may be a spot in the application where you can mention you know an alum and how you know them, though. If not, you can mention at a visit.