Any hotel on lower Canal (south of I-10) should be fine.
Maspero $12.99 for a seafood sampler plate that includes a ton of calamari, shrimp, catfish, fried oysters. Across from Jax Brewery. Bring cash, they don't accept credit cards. A plate like that here costs at least 29.
Garden District via Streetcar Ride from Canal through the Garden District to just past the Audubon Zoo. An experience itself.
Cafe du Monde A must on everyone's list
Ferry Ride the ferry to/from Algiers or Gretna for great scenic shots of the city from the river. Free for pedestrians. Plan on standing the entire time because those old plastic seats are dirty. The ferry docks at the end of Canal.
Bourbon Street Many bars have 3-for-1 beers until around 8pm, you'll pay $7. Every bar has plastic cups near the door. As long as you don't have glass in your hands, you can walk freely with your beer. Three places on Bourbon that you have to see are Marie Laveau's, The Cat's Meow (wave to your friends on the many Earthcams there), and Pat O's (get a hurricane). The locals typically go to Frenchman to avoid the tourists.
Cemeteries Metairie has some of the most picturesque cemeteries. Take the streetcar up Canal to get you most of the way there. Lake Lawn is one of the best.
House of Blues See what's going on there during your visit.
If you rent a car and have time, River Road plantation homes are something to see and take time to get around, but expect to pay $10-20 for entrance to each one. There are a few Swamp Tours within an hour of New Orleans to the southwest along US 90. The Causeway is a 29 mile long bridge with no toll northbound (and either no or $2 toll southbound), you could go north to Mandeville then east to Slidell, then south to New Orleans - from Slidell to downtown New Orleans you will still see abandoned homes from Katrina along Read, Bullard, out to Chef.