Gaussian is a pretty solid program. The input files are easy to write, and it's popularity make it easy to find support. It is a commercial product, though, which can be a problem if your on a tight budget.

Several years back, I tried Gamess, which worked fine. Its biggest drawback for me was writing input files. It was cumbersome to use mixed/custom basis sets, which is probably key for anything you'll be doing for EXAFS. I haven't tried Gamess recently, so the situation may have changed.

I hear good things about Orca as well. I think this package does a lot of interesting stuff related to XAS, but I haven't spent much time with it. A couple years back, Orca couldn't do analytical frequency calculations, which, in my experience, led to very slow frequency calculations. However, according to the website, it seems like that feature will be coming soon, so I would like to find some time to really play around with this program again. 

My colleague uses WebMO, which is a web-based frontend to many electronic structure packages. I haven't used it myself, but it may make for a more unified experience for many of these packages. 

Just my two cents... Good luck.

Ryan