Exciting!
Hopefully I can help; I'm a freshman at Tulane University in New Orleans from out of state, so I've done a good deal of exploring the city this year. I'll list some ideas of things to do in this post, but let me know if there's anything else I can help with beyond what I mention here!
A note on directions:
Because New Orleans is situated on the river, it has a much more organic (and sometimes confusing) layout than a grid-style city. Because of that, streets rarely align North-South or East-West. Consequently, people more often refer to directions as Uptown (roughly west), Downtown (roughly east), Lakeside (roughly north) and Riverside (roughly south).
Within the French Quarter:
-There's a Voodoo museum that's an absolute must-see for haunters. It's a very small place is but jam-packed full of relics and is definitely worth the small charge:
https://plus.google.com/112058245974618645100/about?gl=us&hl=en
-Bourbon Street is Bourbon Street. It's certainly a bit of a novelty at first, but is very catered to tourists. Essentially, it's Vegas transplanted into New Orleans: fun, if that's what you're looking for, but not at all "off the beaten path" as you said.
-Royal Street runs parallel to Bourbon and is more of an artsy street. You'll find all sorts of galleries, antique shops, and a generally less drunken version of the French Quarter here. Jackson Square, which sits at the center of the quarter (and which I guarantee you won't be miss), also has a wide array of interesting artists and musicians on a daily basis.
-Because of the placement of hotels and shops more on the uptown (West) side of the Quarter, the downtown (Eastern) side of the quarter sees only a fraction of the foot traffic of the uptown side.
-Just downtown (East) of the Quarter and within walking distance is Frenchman street, home to arguably the hottest live music scene in the city. If you're looking to drink on any given night, I'd recommend Frenchman Street a thousand times over Bourbon.
-And of course, as you mentioned, St. Louis No. 1 cemetery sits just outside the quarter.
Outside the French Quarter:
-I haven't been, but have heard from friends that the World War 2 museum is absolutely superb. Apparently they have a 4D cinema experience that is worth the price of admission alone.
-The garden district is full of 19th century Anglo-american mansions that are absolutely marvelous to look at. Even if you don't have a rental car and are staying near the French Quarter, getting uptown from there is relatively straightforward on the Saint Charles streetcar line.
-Also uptown from the Quarter (and I believe in the Garden district) is Lafayette Cemetery No. 1. It doesn't have the fame of Saint Louis No. 1, but is equally as beautiful (and FREE) and is worth the stop any time you're in that part of town.
Concerning RESTAURANTS:
-Basically, anywhere you go in a city like New Orleans is going to have good food; there's just too much good competition for bad restaurants to survive. The one situation where you might find a less than great restaurant is if it feels exceptionally touristy (namely, in the French Quarter). Most of the city's restaurants and bars get their business from repeat customers, but there's a few that target one-time tourists and thus don't have to give people as delicious of a meal to stay in business.
-If you want to see some alligators, sign yourselves up for a swamp tour. Fun fact: alligators are highly territorial, so the companies who run the tour can almost guarantee that you'll see gators on your tour because they know exactly where to find them. You won't have to go that far either; most of these places are just 15-30 minutes outside the city.
I hope this helps! Let me know if there's anything else I can help with.
-Collin
