About 20 miles outside of the city are the plantations. Of all the plantations around this area, the best ones are Oak Alley Plantation, Nottoway Plantation (this one is further out, about an hour to hour and a half from New Orleans). And if you have the time, I would also suggest that you take a trip to Natchez, MS where there are lot of historical mansions.
If you are into nature photography, definitely take a swamp tour and you should be able to get a few good shots of the alligators. I've liked Honey Island Swamp Tours and no i'm in no way affiliated with them.
Jean Laffitte National Park is a great place for nature photography as well. And if you want to get some good sunset shots, all you have to do is drive on the Causeway (and driving on the causeway during rush hour can be a royal pain in the wrong place!) and use one of the turn arounds to park your car and get your shots.
If time permits, take a walking tour of the historical garden district. You can get some good shots of the mansions that are located in the garden district.
Hope that helps! Good luck and I hope you enjoy your stay!