I have two:

Take a GUIDED tour of New Orleans cemetaries, especially where Voodoo Queen, Marie Laveau, is buried. She is buried in St. Louis Cemetery # 1. Lots to learn about the cemetaries.

And a guided tour of the plantations outside of New Orleans. I toured one restored and one not.

The Court of the Two Sisters restaurant for Sunday brunch. Bring your appetite. Of couse, do go to Cafe du Monde and have some coffee or cocoa with their powder sugar laden square donuts.

And be sure you have a muffeleta, at the bar across the street on the corner from Cafe du Monde!

Think it is where the muffeleta originated, if I have the right place in mind. Or ask someone for that particular place, someone will know.

And ride the trolly down Canal Street.

Go to Mulate's great food and be sure to go in the evening when the live Cajun band plays, the whole family goes and every one dances. You get a good immersion of the culture. It is hard to find any of the true down home places it has become so commercial.
Mothers for breakfast, also cafe du monde original for coffee and beignet
http://www.mothersrestaurant.net/
Check Chucks website he has great recommendations.
http://gumbopages.com/

Here is a link that might be useful: Mulates

Warning: Only have 1 Hurricane!! (the drink)
I speak from experience.

I was in new Orleans many years ago on business for my employer, and I haven't been back since, but I'll relay what little I know about the place. Our business was with a shipyard and we stayed at a motel just off the French Quarter.

About the statuary: There are several statues of Civil War Heros. My host was quick to point out that the rear end of the horses pointed north. He did not know if this had a significance or not, but thought it was a humorous observation.

During WW2, chickory was used as a coffee substitute and many of locals came to prefer it to coffee. (Chickory has a bitter flavor compared to coffee.) After the war, consumption of chickory continued. So if you should enter an business office and see two coffee pots on the table, beware that one may be chickory. Ask before you get surprised. There are some who delight in seeing a northern novice take a sip of chickory thinking it is coffee.

Mock turtle soup: As the name implies, there is no turtle in it; Authenic mock turtle soup is made with rats. During the war of 1812, New Orleans lay under seige. Food became scarce especially meats. The chefs cold not get turtles, but noted a plentitude of rats in the alleys. They captured rats and used then in place of turtles, hence the name, "mock turtle soup".

But while there, do partake of local dishes. These are wonderful. Crab meat dishes may be heavy with crab oil. If your system is not accustomed to this fare, go easy on the amount you comsume or you may become sick at the table.

Walk the French Quarter and pop in at one of the many hotel lobbies/resturant for a bite to eat. Bourbon street has a lively night life. You can get a feel for it without entering any of the dives. They let your see enough to entice you to enter.

If you stomach is brave and made of cast iron, eat raw oysters from a street vendor. The standard sauce is 50% ketcup and 50% mustard. Live oysters are kept on ice and shucked out in your view. TIP: The oyster should be alive when shelled out. A meat of a good oyster has a dark spot near its center that fades soon after opening. Refuse the oyster if the dark spot is missing.

There is a district in the central city where ante bellum houses have been kept historically correct. These wonderful buildings provide photo ops.

As the poster above recommended, do learn about the burial practices in cemeteries. The water table is at ground level which affects burials. The above ground crypts have 'pull boards'. Ask what these are for.

A few other places from Chuck's page that I also recommend.

Mid-City Lanes Rock 'n Bowl, 4133 S. Carrollton at Tulane.
Perhaps the only bowling alley that regularly books bands, plus serves great food like alligator po-boys. A not-to-be-missed experience. Local acts, blues, roots music and zydeco predominate. Zydeco night on Thursdays. If you bowl, you have more room to dance than on the dance floor. FUN FUN FUN place and great music.

Tipitina's, 501 Napoleon at Tchoupitoulas, 895-8477.
A great club, and a veritable shrine to Professor Longhair, after whose signature tune it was named. Many local acts, plus national touring acts who tend to plkay much larger venues in other cities. Fais-do-do with the Bruce Daigrepont Cajun Band most Sundays, 5-9pm, with free red beans and rice. Food available, plus Abita Beer on tap. Tip's has fallen on harder times of late, with lots of their usual acts now playing the House of Blues. At the Jazzfest 1995 Cowboy Mouth show, Tip's crammed so many people into the club that for the first time I found the concertgoing experience there truly unpleasant. I imagine it's not as bad during the rest of the year, but if you go to Tip's when a bigger act is there, go early. Bookings 523-1614. Concert line 897-3943. Tip's Records 891-7994. FAX 891-7996.
It has become more commercial because it has become so well known so it is not like it once was but still a fun spot.

The original Muffa shop! I must have my Muffa!
Central Grocery, 923 Decatur St., French Quarter.
Owned by the Tusa family, this is the home of the famous muffuletta sandwich: ham, genoa salami, mortadella, provolone, seasoned olive oil drizzled on the inside of the specially baked seeded round Italian loaf, and the crowning touch - a marinated olive and vegetable salad in a thick layer on the sandwich. The pinnacle of the sandwich-maker's art. There are plenty of places that serve muffs, but Central was the first and is still the best. Don't try to eat one of these by yourself, or it could be incapacitating. Or what the hell, be a pig and do it at least once. This is also a terrific little Italian grocery store, with lots of imported products.

I already mentioned Mothers but here is more about it
Mother's, 401 Poydras St. at Tchoupitoulas, CBD.
Many call it the best po-boy joint in town, home of the "Ferdi Special": piled high with their baked ham (the best anywhere), roast beef, gravy, and roast beef "debris" (the little tiny bits that fall off the roast beef and float in the gravy as it cooks). Fantastic breakfasts (try the ham biscuits), jambalayas and gumbos, and the best turtle soup in town (better than Galatoire's). Worth the wait in line, anytime.

and the one not to miss
Mulate's, 201 Julia St., Warehouse District. 522-1492.
A huge dance floor and nightly live Cajun music by the likes of Steve Riley are the major draw to "The World's Most Famous Cajun Restaurant", which originated in Breaux Bridge, La. And hey, the food ain't nothin' to sneeze at either. Large quantities of tasty food, and any place that gives you a choice of frog's legs done two different ways is OK in my book. And you can dance off some of those calories while you're at it, too.

Some of my dear friends were taking a trip down South and asked me this same question and I said top of the list Mulate's and go at night when a band is playing. They came back and told me that was the hilight of their trip! They were so amazed to see from little children to very old folks up and dancing to the great music. You leave with a smile and dancing feet.

For a more real experience get off the commercial path and down into some of the smaller towns that is where the best food is.
I also personally love the flea market at the end of the line.

Helpful New York Times travel article, 36 Hours in New Orleans. Copy and paste this link:

travel.nytimes.com/2012/02/19/travel/36-hours-new-orleans.html

Should keep you busy....

I was there for a short trip a few years ago. Had the opportunity to have brunch at Brennans in the French Quarter. A wonderful meal ($$$$), but enjoyed immensely.
I had milk punch, turtle soup, shrimp sardou and banannas foster. Once in a lifetime...
You must make a reservation!

Here is a link that might be useful: brennans

Bring your appetite. If you arrive in the afternoon or evening, try and oyster bar for dinner - both Acme or Felix's on Iberville are good. Get up early and walk the quarter on your way to Cafe du monde. Try a Poboy for lunch - Johnny's on Saint Louis is great - but maybe only have a half. You will want to save room for dinner - Maybe NOLA (I was there years ago and it was great) or Mr. B's Bistro. Check out trip advisor for some thought ful reviews.

I'll be interested to hear about your trip. I always wanted to go the NOLA and we may just do that sometime this year.

New Orleans is a wonderful city; when I go I insist on staying in the French Quarter even though there are lower priced hotels on Canal St.(which is technically on the border of the French Quarter) or the Central Business District - the neighborhood doesn't have the same "feel" as the French Quarter. To make it more confusing most of the places I'd want to stay in the French Quarter are not chain hotels. When I go I look at the maps on Expedia to make sure that hotel is located in the area where I want to stay. Beware Rampart Street. They will advertise themselves as being in the French Quarter (they are the northern border of the Quarter) but that is the "diciest" area and I would never, ever consider a stay there. I have walked the street in the daytime but would not walk it at night. However, the rest of the French Quarter is well lit, busy and relatively safe if you use your common sense. The last hotel we stayed at is the Bourbon Orleans Hotel, right on the corner of Bourbon and Orleans. Great location. We loved being able to walk out of the hotel and just wander to our hearts content.

Besides walking up and down every street in the Quarter (I'm a photographer at heart!) we loved going to the Garden District and for a ride on the St. Charles Streetcar. St. Charles St. is full of beautiful mansions, built by the Americans who came to New Orleans after the Louisiana Purchase. You can easily cross Canal Street at Bourbon and walk one block (Bourbon becomes Carondolet) which is where you catch the streetcar. You'll stop at the Kiosk on Canal first and purchase your pass for a few dollars. The streetcar is packed full on weekends so if you can do it, please try for a weekday.

You really need to post lots of questions on the Tripadvisor forums. People there will be eager to help you answer specific questions. I always post a lot before taking a trip so I can get the most of what time I have to spend.

Another thing I want to mention is that if you do stay in the Quarter one of my favorite money saving tips is to rent a car only on the last day. You can easily walk to car rental agencies from the French Quarter (last time we used Dollar). We walk to the car rental place (got ours for $62 including tax) then drove to the hotel to check out. Put our suitcases in the trunk then had the car for the whole day to explore. When it came time to head to the airport we used our GPS (airport is only about 20 miles from the Quarter) and it saved us a 30 dollar cab fare plus tip. That way we can explore the things we want to out of the Quarter as long as we have an evening flight home. We like to drive out to Deenies for some great seafood for our last meal.

Hope this wasn't too long; I love New Orleans and hope you have a WONDERFUL time!