There are a lot of options near the medical center that have plenty of availability right now.
I'm a rising 4th year, and I currently live at AMLI on maple which is literally a 2 minute drive to campus/the hospitals. I've been here a year and I truly have no complaints at all, security alarms come standard, security guard overnight + cameras in common areas + garage, key fob access to everything, great resort style pool + super clean and big gym, etc. A little more expensive than some (can get 1 BDR from 1000-1200/month, and 2 BDR from 1400-1700, affordable if have a roommate), but it's a LEED building so super energy efficient; I only pay like $40-50 in electricity. Truly have had no problems here at all. Let me know (PM me) if you're planning on looking here or renting here and I can answer any additional questions you have, and if you put me down as who referred you here, maybe we can work something out in terms of the little referral incentive they give current residents.
🙂 Also, UTSW is a "preferred employer" which counts for students too and gives you no app fees and waved deposits I think.
http://www.amli.com/apartments/dallas/medical-district/dallas/maple/
Also, there is a brand new place right across the street that's slightly less expensive but just opened like 2 months ago. Not quite as nice as AMLI but has a salt water pool which is kind of awesome.
http://thesouthwestern.com/
Other places I know current students live and have liked include:
http://www.21fortymedicaldistrict.com/Neighborhood.aspx (medical district)
http://www.colonialprop.com/dallas/colonial-reserve-at-medical-district/ (medical district)
http://www.cityville-apts.com/apartment_communities/cityvilleOakPark-Dallas/ (on lemmon ave)
http://www.mqcedarsprings.com/ (uptown)
http://www.amli.com/apartments/dallas/uptown/dallas/knox-henderson/ (knox henderson, other trendy neighborhood with bars/restaurants, less expensive than uptown, less chaotic)
http://www.amli.com/apartments/dallas/uptown/dallas/quadrangle (uptown)
http://www.5225mapleapts.com/ (medical district)
I would avoid the Design District (tons of really shady crime, like serious stuff going on) and I would avoid living on the East side of 75 near/between Haskell and Fitzhugh (you WILL get your car broken into, no matter what, it will happen), even though the Haskell/Fitzhugh area is actually really cool for going to fun bars and restaurants, living there is just a mistake IMO.
Hope that helps some of you guys!