You will probably be fine. However, if you do move to Uptown New Orleans you should be willing to accept that there is crime. One of the prior posters seemed to indicate that the neighborhoods experiencing crime problems are far afield. I would respectfully disagree with that. Central City is just down St. Charles Avenue from Tulane and its residents have endured a lot of murders. Also the neighborhoods west of S. Carrollton Avenue have had crime problems traditionally. So, really there are high crime areas quite close. One option is that you commute to Tulane. River Ridge (in adjacent Jefferson Parish) would probably be a good choice because you can drive down the Earhart Expressway -- it's a short commute. There is a big apartment complex out there called the Creeks. This is a safe suburban area.
On the other hand, if you do live near Tulane, you will most likely be fine. Violent crime does happen occasionally and you do need to be careful. However, there are lots of people living uptown and they're quite happy and feel fairly safe. And it's a beautiful area.
I would suggest that you look at the New Orleans Police Department's Crime Maps and enter the zip codes -- 70118 and 70115 -- for the uptown area. You can get an idea of what's going on presently.
Go to
New Orleans Police Department and click on Crime Maps. If you choose Search by Boundary you can enter zip codes.