I lived in New Orleans for two years. There are some very bad spots, usually right next to the very good spots. The French Quarter, for example, being a tourist magnet, attracts a lot of pickpockets...but it also is an exciting and lively place. It's also fantastic for music--don't miss Preservation Hall on St. Peter St., where they play old-timey jazz. Very hot. There is also, (or used to be) a free newspaper listing all the music and performances for the weekend, you should be able to find some music to your liking. Cajun, definitely, but everything else as well.

I would suggest that you ask at the hotel or wherever you're staying, about the current bad spots. They'll be happy to suggest places to stay away from. Keep your wits about you, don't walk around Bourbon, Basin, or St. Peter Streets drunk, act like you know where you're going, don't flash a lot of cash. (Those are pretty much good rules for any big city.) As for smaller towns nearby, Metairie is a nice place. And if you are driving through Louisiana anyway, see if you can work St. Francisville into your plans. It's in the north of the state, and has some absolutely gorgeous plantations.

Whew! I was on fire there for a minute. If you have other questions about N'Awlins, feel free to PM me. I'll answer if I can.