I am currently a resident of the New Orleans Consolidated Statistical Metropolitan Area (way out in the sticks), but before Hurricane Katrina had lived in a close-in suburb (i.e., Meraux, in St. Bernard Parish). And during my Katrina diaspora days, I lived in Arvada, CO near Denver.
Since Katrina, the cost of rentals in New Orleans proper (not counting the really rough ghetto neighborhoods) has gone through the roof; you'd have to have a roommate. I would recommend finding a rental in my old parish, but you don't have a car. Fortunately, it seems that the timing for your time in New Orleans matches with the summer break for Tulane University, so I would presume that there are empty rooms in current students' apartments. It sounds like you will be attending the LSU Health Center, so you could get a dorm room that way, and be right there. New Orleans also has a decent hostel scene, and you could probably negotiate a good rate for staying so long.
For a few months when I had to be back in the area before buying my Katrina replacement home, via Craigslist I found a room with someone way out in the sticks, but I could have gotten such a room for about $1K a month in the prime Uptown area. Be forewarned that there are some crazies out on Craigslist, like one guy that wanted me to give a urine sample (WTF?), and the gal that was a Wiccan that did ceremonies at her place.
As for Boulder, it's always been expensive, but I would presume that the situation at the U of Colorado there would be similar to that for Tulane U.
Good Luck!
