Hey!
I'm a 4th year at Tulane, and going into psych, so I can try and give you a little info on the program, if you want more details, feel free to pm me.
The psych department did take a pretty big hit after Katrina. I'm not sure the exact number, but I'd say about half? However, the faculty that is here is very committed to being at Tulane and in New Orleans. Honestly, every attending I worked with was great, and provided a lot of teaching, both to students and residents. The new PD who started last year is young and enthusiastic, and I think he will be a real asset to the program. They also have several younger faculty members who have come on since the storm, which I think keeps things fresh in terms of learning.
The residents at Tulane seem to love it. I'm pretty sure it has one of the most chill call schedules I've seen. One of the inpatient sites is in Mandeville, which is about 45 minutes from NOLA, across Lake Pontchatrain. I think you only end up spending 3-6 months there total, and there's no call out there (unless you are moonlighting). I actually think the site is an asset, as you see a lot of variety in psychopathology, and they have acute units, long-term units, and child units at which to rotate. Pretty much everything else is done in NOLA.
Downsides: Tulane does not have a dedicated psych ER. There is a behavior health unit at University (Charity) that is run out of trailers. I'm not sure if plans for the eventual new charity hospital include a psych ER or not. It is a smaller program, and there is less faculty/research than before the storm. However, there is research available, and if you are interested in that track I think you wouldn't have a problem finding someone who would be glad to take you on.
Strengths: For its size, New Orleans has a huge population of chronically mentally ill individuals. Even coming out of med school, I feel like I've seen a lot of stuff that I may not have seen other places. Residents are really nice, super laid-back program. They also have med-psych, triple board and psych-neuro programs, so you get to interact with residents/faculty in a variety of specialties. And New Orleans is an AMAZING city to live in.
Anyways, this was really long, but feel free to let me know if you have other questions. Good luck!!