New Orleans is indeed a seedy place but it is also an amazing trip. There's something about New Orleans that you won't experience by visiting any other American city, (other than the public drunkenness)!

I would recommend everyone visit New Orleans at least once but definitely be alert, and do your homework before you go. Current travel books will give you tips - for example, 1) since N.O. is below sea level, they do not bury people underground; they are all in mausoleums, and there are some of the most amazing grave-side statues I've ever seen. The cemetaries are interesting enough that they do cemetary tours. BUT - under no circumstances should you stroll through the cemetaries alone or even in a very small group as they are known to be places of muggings. 2) N.O. streets are very mixed. You could be on a beautiful street and turn the corner onto a dangerous street. It seems that safety level in New Orleans varies sometimes from street to street rather than from neighborhood to neighborhood.
So anyway, grab a travel guide, read up, and go ahead with your plans. As long as you have the information you need ahead of time, I don't think you'll be sorry that you went. To the contrary, you may end up being thrilled to have experienced such an interesting place.