Safety: If you stay in the French Quarter and financial districts you should be fine. It is typically recommended NOT to visit the cemeteries outside the Quarter without a large group or tour. I Have visited the cemetery that is just outside the Quarter during the day with a small group without incident, though there were many other tourists milling about. Just be sharp eyed and aware of your surroundings when on the outskirts.
Duration of stay: I typically stay for 3-4 nights, as the French Quarter can be exhausting, yet I always wish I had one more night :)
There are tons of tours. The plantation tour is nice. I recommend AGAINST the ghost or haunted tours of the French Quarter. BOOOORING.
The French Quarter is the safest place. I usually stay at the Bourbon Orleans and have always had a great time.
Food: Even the bad restaurants are pretty good in new Orleans. I try to avoid dining in the restaurants on Bourbon. Check out the streets that run perpendicular to it and down towards the waterfront for many a hidden gem. Some great cheap eats are Poppy's diner and The Gumbo Shop. Two of my favorite bars there are The BlackSmith on Bourbon and Mollys at the Market.
Music: I'm not an expert, but on Bourbon, many music clubs advertise no cover, but expect you order a round of drinks every hour or during every set that the band plays. Often you can just hang out and listen outside, and there are many talented buskers.
Shopping: Royal Street, which runs parallel to Bourbon, is full of nice antique shops and art galleries. Also there is much shopping near the waterfront, including the famous French Market. Also look out for some cool voodoo shops.
Have fun!
-DonPaul


