Getting from the airport to downtown or French Quarter could not be easier. The taxis are well organised immediately you leave the baggage claim area and the best part - its a fixed fee. From the airport to the French Quarter is $33 for 1 or 2 people (and the same on the way back) as of April 2013. The cabs will take cash or credit but make sure the driver's credit card machine is working.
The Jefferson Bus 2E takes you from Louis Armstrong Airport to New Orleans. The fare has been increased to $2 - still a bargain campare to $15-20 for a shuttle bus. You can download the bus schedule by going to the RTA website. You board the bus on the upper deck near the DELTA stop. Take the bus to the end of line - which will drop you off at the intersection of Tulane and Loyola. From the bus stop, walk left on Loyola 1 block - that brings you to Canal Steet. one of the two main drags in the French Quarter. Take a right turn on Canal, and chances are, any hotel in the FQ you are staying at, is off this street ( or not far from it).
The prices for taxis have gone up a bit in the last year from $28 to $34 from the airport. But if you have at least 2 people it is still the best, quickest and most cost effective way to get into town. The shuttle buses take much longer and in some cases will only take you to certain stops downtown. Before Katrina, when we owned a B&B here, we looked down the street one day to see two of our guests hoofing it down the street hauling their luggage along. They told us the shuttle bus driver refused to take them the 6 blocks from Canal Street to our place, so they had to walk. I recommended the taxi to people after that.
For the few extra bucks (compared to the shuttle) the taxi is worth it.
As to renting a car, hardly worth it. You can walk everywhere in the French Quarter and there is virtually NO parking there. Oh, you might get lucky once in awhile but not worth it. If you figure the cost of renting a car and paying $30 a day to park it at your hotel to be at least $80 a day, you would be hard pressed to spend $80 a day on taxis. Even running back and forth to the Garden District and Uptown for some of the restaurants and tours, and certainly not for buzzing around the Quarter if you don't feel like walking. Particularly if you have at least a party of two to split the cost of the taxi.
Another consideration is drinking and driving, frowned on here even with our easy going view on drinking. In addition, I never recommend walking outside the French Quarter at night. Taxis here will not give you a hard time for taking a Taxi a few blocks from one side of the Quarter to your hotel that may be a few blocks outside.
Lastly if you happen upon a great cab driver who has lived here for a long time ask him for some recommendations for where locals eat/drink/hang out/hear music. We did on our first visit here and our driver recommended Maple Leaf Bar off Carrollton Avenue (a pretty far distance for most tourists from where we were staying). We probably would have discovered it eventually after we moved here, but God bless him for directing us to one of the top 3 places in New Orleans to hear some of the greatest music you will ever stumble across. We have been going there regularly for the last 6 years.
Enjoy your visit to New Orleans, we enjoy living here every day!
For $30.00 round trip (or $15.00 one way), the highly efficient and professional will take you from the airport to your destination. There is a ticketing booth in the baggage claim area where you can pay for your fare; the shuttle will be directly in front of you once you exit the airport.
They do provide handicap access but they request you call in advance.
I've provided the number and website below.