No you do not need a car. Having a car is a pain as parking is limited. When we go to New Orleans we parked it in the public parking garage next to our hotel and left it the duration of our trip. It's so easy to walk or grab a cab. Moving your car to find a new spot, pay for a new spot, etc. is a waste of time. If you are flying in, just grab an airport shuttle to the hotel. You can schedule an airport shuttle in advance if you would like.
I always drove to New Orleans so I don't have experience with their airport shuttles but have used them at other towns and I found it cheaper to shop around in advance and make a reservation. For example in Ohio, we made reservations in advance and I got a military rate. Looking for our shuttle there was a shuttle line ran by the airport that charged not only the shuttle fee but an airport fee for them using the line and having airport staff help you in your car. LOL. I did tell airport staff I called and made reservations and he kindly pointed me in the other direction where the reserved cars usually waited. That was nice of him. He was also the one that explained their charges of being higher than reserving a car.
My suggestion is do not just say the name of your hotel. Say the hotel name and street every time you make a reservation or get into a taxi. There are multiple hotels with the same name. For example we stayed at the Marriott and there were about 3 other Marriott in the general area. The names varied from Marriott French Quarter, Marriott Courtyard, etc. but I find it better to say Marriott across from the Convention Center (Convention Center Boulvard).
Have fun! Make sure you go to Cafe Du Monde with cash and seat yourself. There is seating inside near the bathroom that many do not know about so if there is a line for self seating outside, sometimes you can check inside and there are a couple empty tables. We have a tradition of going to Cafe Du Monde at midnight with our kids. It's safe as that is where all the police officer park their cars! I always feel safe in the general area of the French Quarter. Lots of people everywhere. It's some of the dark side streets that I start to feel uncomfortable late at night.
We love dinner at Muriel's.
http://www.muriels.com/ I don't care for their lunch courtyard menu.
We also enjoy breakfast at Mother's but some find it very old and not up to par with what they are use to but it's a local favorite. I walked the several blocks from our hotel to Mother's instead of taking a taxi.
http://www.mothersrestaurant.net/
New Orleans Hamburger & Seafood Co is good.
Never ate here but have walked past it. DH says it's famous and very upscale.
http://www.commanderspalace.com/ You will need a taxi from the hotel to here as it's not in the main French Quarters area. It's about a 10 minute taxi ride.
I would avoid Cafe Maspero. We have ate there on several occasions and never happy with the food. Our last trip was a group trip for my daughter's cheerleading and the team mom picked this spot.. DD had to go there as the team event was mandatory, DH and I went to Muriels. We have had enough and afterwards the parents that stayed said they did not enjoy their food and the girls didn't really like it either. It's pretty popular but I just think there are better places to eat.
Also if you have a smartphone and want to learn more about the French Quarters in a scavenger hunt kind of way, look at purchasing "Stray Boots" French Quarters Walking Scavenger Hunt game. We did this with the cheerleaders. Hint... the last top is Cafe Du Monde! You have a year to finish the game and can start and stop it throughout that year, so you are in control of how much you play or if you decide to change your route and go a different direction.
