I currently live in New Orleans and have been doing so for 6 years. I think your best two options are to call a real estate company uptown or look in local weekly paper The Gambit. I've always gone through Latter and Blum (on Maple St.) Call or email them with what you want, and they can go through all the other companies properties and pull a bunch to show you, and can even email the specs to you with pics for many. The most important thing to do, is a
drive by. The neighborhoods up town can change from million dollar mansions to ghetto crackhouses in two blocks some places. The rule stated about about between Claiborne and the river is a good rule, but there are some places north of claiborne that are good, just as close, and a bit cheaper.
The Gambit (look in the Uptown/Garden District section, you have to scroll a bit) can give you some of the best places in the area. However, these papers are placed for free in coffee houses and such Sunday mornings. Get one then and get on the ball cause the best places will be gone quickly. This can also happen when going through real estate agents, the best places on the market here move. So be on the ball, and don't really bother looking till right before you come down. Some apartments will put notices up now, and some will only go a month ahead of time. If you want a single and don't want a dump and to be relatively safe, expect to spend $550-750 on rent alone unless you get a roommate. I pay $800 now for my one bedroom, but I have a prime location and it is very safe and big.
One other thing, if you are a guy, and like the frat scene, Tulane has a house of ~13 guys right by the campus and popular freshman bad (got to love those young hotties, right?) I think it is somewhere around $350 a month. You should get info about this place too.
If you have any questions, please feel free to pm me, I know what a hassle finding a great place can be. If you need an opinion on an address, I can do that too.
Good luck!
(Oh, and if you need some good places to eat, I can help with that too, since there is a wealth here. I am sad I am going back to Texas soon, the land of Chilli's and such
🙁)