To add a bit to this housing discussion - I agree that NOLA is a perfectly safe place to live. I live near what I'd honestly call a "borderline" area and have been fine for the past year. By borderline, I mean my street and area right around me is patrolled by private patrol but the next block over isn't and had some crime over there.
The key is just to check the area out both morning, afternoon, and night before signing a lease if you're nervous. Knock on the neighbor's door and ask them about how they feel the neighborhood is. If they won't answer the door in fear, maybe that's a bad sign...; but most likely they will ease your fears.
Parking near Tulane is possible. If you have early class, St. Charles is an easy walk to TLS and beautiful, but you need to be there around 8am to stand a chance at a spot. There are a few streets near campus where parking dept does not patrol (mostly dead end streets) so those are possible, but I park there daily, so don't steal all my spots!