I've been 4 times- spent a week there this year. Supreme Commander gave you a nice run down. I'll make a couple of additions.
For fun tours, take a trolley up to the garden district. You'll pass the manning house. Sign up for a Ghost/Voodo Tour. Consider an airboat swamp tour to see some gators. A true New Orleans tour guide can't be beat. The people down there are incredible storytellers with a great sense of humor. The best storytellers in the world are either Irish or Cajun.
Most people who go to New Orleans love the Cats Meow on Bourbon. A unique karoake bar if you like that sort of thing. They have a big stage with an Emcee who keeps the crowd rolling.
Pat O'Brian's is the most famous bar on Bourbon. It actually has a great outdoor garden and is worth sitting in for at least one Hurricane. In general avoid all the disgusting insanely sugary drinks on Bourbon St though.
Preservation Hall is right nearby, and is one of the most famous jazz venues in the country.
Tipitina's is great for a music venue as well. Check in advance for what shows are playing as you will need to get a ticket.
SupremeCommander did not steer you wrong with Frenchman St. More of where the locals hang out and a great vibe overall. Try out dba as well. There's a couple of dba's here in NYC (they were originally affiliated), but the one in New Orleans has great music + great beer.
For food, you can't beat New Orleans. Everyone will tell you to go Cafe Du Monde for Beignets and Central Grocery for Muffaletta's, and those are really good places but the lines are often pretty long. You can get great beignets and muffaletta's elsewhere too.
Napolean House- great casual bar/restaurant for a Muffaletta and bloody mary. Difference between the Muffaletta (btw, a Muffaletta is just an italian sub on a round loaf with olive spread) here and central grocery is hot melted cheese vs. served cold.
SoBou- fancier restaurant in the W hotel in the French Quarter. Go here specifically to try the sweet potato beignet with foie gras sauce. Amazing!
Mothers- The best restaurant for PoBoys. The Ferdi special with cheese is amazing. Like a combination of a Cuban Sandwich and a french dip. If you're going with a friend, get a oyster and shrimp po boy and split the two sandwiches.
Cochon- to me the best restaurant in New Orleans. Casual atmosphere, but absolutely top notch creative cuisine.
Bayona- a bit fancier, but just phenomenal food. Slow food philosophy.
Brennan's- they invented the Bananas Foster. Famous for breakfast, but good for a fancy dinner or just dessert.
Emeril's- famous obviously, but actually great food and great steak.
Galatoire's - this is a straight up New Orleans creole spot. One of the famous old spots. Go for lunch and as for a waiter named John Fontenot. One of the funniest, most unique waiters ever. A classic New Orleans experience.