Hattiesburg and Leesville are the only two locations with sizable installations away from the coast. Hattiesburg has a fair number of National Guard folks training for deployment to Iraq, but they could probably accommodate some refugees. They may be stretched, however, just getting their own folks under cover. That area is going to have its own storm related problems.
Leesville would probably be the best bet, but it isn't exactly easy to get to from New Orleans. Beyond that, you are talking about Shreveport or Meridian (which certainly doesn't have adequate facilities).
Or were you referring to the military facilities in metro New Orleans?
Ft. Polk is 40 miles west of Alexandria. They would have to establsih a tent city there to hold the people.