Memphis is pretty well covered in an earlier response, but I'd add Elvis's home Graceland, which is pretty interesting in its own way.

New Orleans - The French Quarter is so fun to photograph, at its best early. Get out by 7 or even earlier to get the sunrise striking the St Louis Cathedral (shoot from the balcony area of the River Walk), and to watch the city wake up, the locals walking their dogs, the street mimes, musicians, carriage drivers and vendors setting up for the day. Go to Cafe du Monde as soon as the patio opens and go back late after the crowds thin out. Take your camera to restaurants and ask for patio seating. Go to Preservation Hall. Shoot the oyster shuckers at Felix's, Acme, or Bourbon Orleans. Ignore Bourbon St, there's plenty of other streets to explore that are less touristy. Go to the French Market. Walk Canal St to look for 50's type stores and neon signs. Take the streetcar uptown to Carrollton and back, and if you're inclined get off at Tulane/Loyola/Audubon Park to walk and shoot. Visit the cemeteries but not at night (can take a tour to assure you're in a group). Go to the WWII museum and the Aquarium. Take the car ferry to Algiers and back to get good shots of the city skyline over the river. Magazine St and City Park are other interesting areas to explore. I've never felt afraid in New Orleans, I've lived there and I visit regularly, but if you by chance find yourself having turned into an area that looks unsafe, just turn around and go the other way. Take a swamp tour to see alligators, feral hogs, water birds and other wildlife. Take a plantation tour or drive the River Road yourself, the plantation estates are fascinating.

If you're driving from one city to the other, consider making the drive part of your adventure by including parts of either or both of these: the Natchez Trace, a national park scenic road that has wonderful scenery and historical sites from Indian mounds and pioneer homesteads to mansions and civil war battle sites. And/or Highway 61 that runs through the MS delta and roughly follow the Blues Trail which has unusual photographic opportunities for those willing to look a little deeper - much to see though not the grand-landscape type. But if you do this route, you've gotta hang around long enough to listen to the music, too (Clarksdale is a good bet for that experience).

For New Orleans, some of the previous posts cover the main sites. I would take a trip to the Audubon Zoo. It is a world class zoo, with all the animals in close to realistic enclosures. Plus, Mississippi River Park, behind the zoo. Of course Audubon Park, which in front of the Zoo, and Tulane University just on the other side of St. Charles Ave. The best way to get there is ride the St. Charles Street Car, which may be disrupted by construction, with a bus half way down the line. The St. Charles Line has green cars, the Canal/City Park line has red cars. Take the "Red Line to City Park, and see the sites there, Art Museum, Lakes, (lots of ducks and swans) the Sculpture Garden, and Botanical Gardens. Also beware, July and August is our hottest months of the year, you may be greeted with temps of 90+ degrees, and 95% or higher humidity. So, carry some water with you. July and August is also the peak time of the hurricane season, so listen to weather reports for local storms. Bring a umbrella, and enjoy your trip.

I live in Memphis and in addition to the earlier responses would suggest that you check out Elmwood cemetery about 5 miles from downtown. It is a historic place dating back to pre civil war and has some great photo ops. Also take the elevator to the top of the pyramid (now Bass Pro shops) for a panoramic view of downtown and the river.check out the old Tennessee Brewery bldg downtown for interesting architectural features. The hernando de soto bridge over the river is a great photo op after dark with its lights reflecting in the river. A great spot to capture this is right at the Welcome center on riverside drive. You can get a shot of the bridge with the boats in the marina in the foreground. Also good shots of the bridge and pyramid from Beale street landing at riverside and Beale.The Harahan bridge ( the old bridge) against the sunset is another great shot.The Dixon gallery and gardens are having a temporary exhibit of large outdoor sculptures through sept. And the grounds are beautiful as well. Right across is the Memphis Botanical gardens.
The national ornamental metal museum downtown on Presidents island is another great place with good views of the river and you may be able to get some shots of the iron smiths working.
Walk downtown along Main St from north to south main, and into the side streets ,you will see many interesting old buildings etc. walk along the Bluff from Beale down to Tom Lee Park for great river views.
Contrary to many opinions Memphis is no more dangerous than other large cities. Downtown is quite safe. As with any other place if you venture into the wrong part of town you may be inviting trouble.

I have been an Elvis fan since 1956. I went to Graceland two years ago. You are allowed to take all the photos you desire, just cannot use a flash. Great tour. You can take all the time you want on the tour, no guides pushing you to move along. The neighborhoods around Graceland are pretty crappy and not too safe. My son and I ate at one of the restaurants at Graceland and the food was okay and not pricey, unlike Disneyland.
The French Quarter offers numerous photo opportunities. It is best if you walk in groups of four or more as the muggings have increased even in the French Quarter. To me, the rest of New Orleans is just another Detroit of the South. Best gumbo in the world is in N.O.