Let me start off by identifying myself as a 3rd year IM resident at Parkland/UTSW who will be starting GI fellowship here 7/1.
I was pretty conflicted as to what I wanted to do as a 4th year so the only away rotation I did was a month in the CICU at the Cleveland Clinic with Eric Topol and Steven Nissen. I did so because I was serioulsly considering Cards as a 4th year med student. I had no intention of wanting to go the the Clinic for IM residency, but if I had done Cards I wanted to be well situated for applying there and to get letters from Topol and Nissen. Good rotation overall, and interestingly, Topol almost became an Endocrinologist but switched to Cards at the last minute, so he was very understanding of my "change of heart" (sorry, couldn't resist)
I do think that in general doing an away at a place you are interested in going is/can be helpful if you do a good job. I would target places that you would consider a stretch as far as getting in for residency, given that you need any leg up there possible, and rotating with staff there and doing well in their hospital environment and getting a letter from staff there (hopefully) can go a long way to putting you high on their rank list. Just don't do poorly there (double edged sword, but worth the risk if you are motivated and will work hard that block).
I don't think the rotation you do ends up mattering a whole lot -- GI, Cards, Endo, Rheum, Pulmonary, Renal, whatever interests you. I do think that from the standpoint of learning about a program and what life would be like as a resident there doing a rotation where you might split time between the unit and the floor might be useful (e.g. Cards or GI consults) versus if you know you are a unit junkie and are Cards or Pulm bound maybe doing a CCU or MICU block might not be a bad idea either. If you think you might be heading toward one of the outpatient focused specialties like Endo or Rheum, consider doing that (for the flavor). Ideally, what you want is to rotate with staff who are well known and connected. Contacting a program's chiefs or current residents and asking them which away rotations are popular, and in particular talking to housestaff to ask which attendings are good to be connected with to get in, can help define what rotation you should take as well.
As far as housing, I think most places can set you up with student housing if there is an affiliated med school with such housing, or email the program director or student affairs office there and they try to hook you up as well. Often times, residents have an extra room or a couch for a nominal fee that month that they could hook you up with.
Hope this helps some. Post, PM or email me with other ?s.