Boy, long subject, but there it goes!
You do not have to travel all over to do your rotations. In the past there were "traveling groups", and the participating students would do rotations in several different places within a geographic region. This is not the case anymore. If you are in the Kansas City group, for instance, you do all your rotations in KC, unless you choose to do some of your electives elsewhere. Not every rotation is at the same hospital, but they are all in the KC area. The same is true for the other rotations sites (the St. Louis group does all their rotations in St. Louis, ans so forth), although some places may have affiliates which are rather far from the main hospital. One of my classmates, who is going to NJ, may have to do some of her rotations in a hospital which is about 2 hrs from her main site, but this is the exception rather than the norm. Some of the more rural sites may include 2 hospitals which are also located a couple of hours away from one another. It is a matter of where you choose to go. Several places will have housing, but you have to request it well in advance.
Now on to the subject of "how to choose a rotation site". It is a lottery. You fill out a paper with your 3 choices; everyone's choice is entered into a computer program which tries to match the most students with their top choice. The majority of students gets their first choice, a small % gets their second choice and about 20 students or so have ended up "unmatched" in the past 2 years. The school works with the "unmatched" students trying to find mutually satisfactory sites. It is also possible to "trade" sites. For instance, if I got a site in Florida and I actually wanted Michigan as my first choice, I can trade with someone who wants to go to Florida but ended up with their second choice, Michigan.
Every year, there are about 65 openings in the Kansas City group. This year we had an unofficial estimate of about 80 people who wanted KC as their first choice.
Everyone I talked to was happy, at the end, with the site they received, but there are no waranties and the school makes no promises as to where you will end up doing your rotations. It is my understanding that the process hasn't always been very smooth in years past, but my own experience, so far, has been positive.
I am staying in KC for my rotations, which start in 3 weeks (hurrah, I can't believe that the first 2 years are behind me!). If you have any more questions about rotations or UHS in general, feel free to ask.