My wife is from New Orleans. Here is her general guide:
The main areas to see are the French Quarter, Uptown/Garden District, and Magazine St. The Lakeview area is nice, but the the lakefront is nothing more than just a drive to view the lakefront (since the hurricane, a lot of the great restaurants out there have closed).
First off, you should be shot if you eat or drink in a chain restaurant like Bubba Gumps, Margaritaville, Coyote Ugly, etc....just don't do it. Pat O'Briens is allowable, and maybe the House of Blues if there is a good band, but that's it!
Restaurants are everywhere. My favorite lately is Restaurant Luke by John Besh. He has other restaurants as well. The Brennans chain restaurants are numerous, including Redfish Grill, Brennans, etc. Still, you can do better. Famous places include Galatoires, Antoines, NOLA (Emeril's), Arnauds, Mr. B's, Redfish Grill. Acme Oyster House is an institution, but you can also get chargrilled oysters at Dragos.
For basic New Orleans sandwiches and seafood, Masperos is good, right across from Jax Brewery near the French Market. Cash only. For tea/brunch, the Court of Two Sisters is famous. Mother's seafood is a great lunch place (on Poydras). Johnny's Po Boys are the best around! A great dive of a place for lunch.
Joey K's on Magazine Street (featured on Diners, Drive-ins and Dives).
Port o' Call on Esplanade is THE place for a huge, delicious burger.
Bourbon street is a mess. Just a bunch of noisy bars, but worth a walk anyway. Lafitte's BlackSmith Shop, a spooky old piano bar, is the only spot we like on Bourbon. It is located down Bourbon away from the Central Business District, close to Esplanade in the area dominated by gay bars. It is one of the oldest places in the city and a neat place to sit in the window and watch the freaks go by.
Favorite bars include Mollys on the Market, Sylvaines right off Jackson Square (great drinks!) and of course visit Pat O'Briens. Carousel bar at Hotel Monteleone is a nice spot. We also love Napolean House...
Preservation Hall, for jazz concerts is next door to Pat O's. Nothing there but music...no drinks, no food..
Cafe Du Monde for Coffee and Beignets. Right next door is the French Market for souvenirs and trinkets.
Also, right across Esplanade from the Quarter is the Marigny district. This area has a lot of hole-in-the-wall jazz clubs and such.
Board a trolley car to Uptown/Carrollton/Garden District. Take the car all the way down St. Charles Avenue to Carrollton. Maybe a 30 minute ride. Along the way, you can see the mansions on St. Charles and could stop at a couple of places if looking for lunch. Recommend the Columns bed and breakfast for a lunch/brunch/drink on the big front porch. Not much else to do here other than take in the sights. This route passes Audobon Park, with one of the country's best zoos, Audobon Zoo. At the end of Carrollton are a few good restaurants, with Camelia Grill being the most famous and serving a world famous breakfast/brunch. Get off, turn around and come back, unless you want to continue all the way down Carrolton to the City Park and the Art Museum.
Commander's Palace restaurant is out in the Garden District...world-famous.
Magazine Street, while not on a street car line, offers some great shopping for antiques and such. It is not too far from the Quarter and Uptown, but you will need a car to drive there. Some really neat little restaurants on Magazine too...a good place to spend a couple hours walking around.
Other tourist attractions not necessarily specific to New Orleans, are the Art Museum at City Park, the Aquarium, and the D-Day museum.
You can venture out to the swamps for a boat tour or walking tour with the alligators...but I have never done that. And, you could always drive through the Lower Ninth Ward if you want to see just how bad things still are after that area was flooded...not fun, but maybe worth it historically.
Finally, be safe. Especially in the French Quarter. It is still a rough area, even with all the tourists around. Also, it is worth picking up a copy of the Lagniappe, the local entertainment guide, and checking out
www.nola.com. The city has over 400 "festivals" per year....