Stay out of the cemeteries, as well. Lots of tourists are intrigued by the above-ground tombs, and the cemeteries are a rich hunting ground for the natives - or at least they were pre-Katrina. The escorted tours may be OK, but don’t go in there on your own. In the quarter, don’t go farther away from the river than Dauphine, or farther down river than St. Phillip. and after dark, subtract a block each direction. Stay sober and aware, and enjoy your visit.
As politically-incorrect as it may be to say, if you find yourself in an area where you are the only white guy around, it's time to leave. Quickly.