I'm an undergrad at Tulane now, and I'm living uptown. If you have a car and are looking for off-campus housing, I live in a pretty awesome complex. Apartments are:
$650 a month + utilities (for a one bedroom: includes bedroom, full bath, loaded kitchen+living room)
$900 a month + utilities (for a two bedroom: two bedrooms, two bath, loaded kitchen + living room + washer + dryer)
$1100 a month + utilities (for a larger two bedroom).
The complex is on S. Carrollton Ave, a pretty major street that runs into St. Charles. There is a street car stop right outside my door, and I am right around a lot of restaurants and stores and coffee houses. You can always take the street car or a bus downtown towards the medical school, but its a pretty decent ride, so i wouldn't really recommend it.
Oh, and parking is either $60 a month in a lot, or $5 per half a year for a residential permit as a student, which is clearly the better deal. There is a little-driven-on side street that is pretty awesome for parking.
Anyway, if anyone is coming down here to check out the town or wants to talk to my land lord, send me a PM and i'll send you his number. Usually at peak move-in times there is a waiting list (that is, beginning of may with the end of the school year or the end of august with the beginning) but if you set something up now, you'll probably get a place.
My landlord also has a few other properties in even better spots (closer to downtown and on st. charles) but for a lot more money ($900 for a single, 1500 + for a double).
Also, safety is definitely something to be aware of in New orleans, but i'm on a major street, and I've never heard of any problems around me. The apartments are also gated.
I have some pictures, too, so PM me if you'd like to see 'em.