Hey GymRat,
Most people live on the west side of town, since it's newer, a little less congested and has more options. Popular apartment complexes are The Tuscany, The Legends of El Paso, The Pointe, and Acacia Park. There are a few others that some people live at as well. I wouldn't worry about it too much yet since the apartment complexes will have no idea what their availability will be come next June/July. Last year a packet went out to future students with reviews of apartment complexes, so that will help you decide as well.
That being said, I don't know if I'd wait until Spring Training to start looking (if it's in late May again). I know several people who seemed a little frustrated with the process having waited that late, when complexes were out of the floor plan they wanted or they ended up on a waitlist. One of my classmates waited about a month after school started before the apartment she wanted became available for move-in. I came on a separate trip in April to scope things out and ended up signing for an apartment then, since I wanted to move in a couple of weeks before school started so that I wasn't unpacking while dealing with orientation (3 weeks, most days from 8-5).