You can then plan what you do from there. Of course, the fact that there have been no reports of tornadoes related to the hurricane doesn't mean that you're out of danger. Your neighborhood could always be the first one that hits the area. Even if the hurricane hits your area during the daytime, the clouds and rain will make it dark outside, possibly too dark to see a tornado as it's traveling towards you. That means the best way you can tell when a tornado is coming is to listen.
Tornadoes make a very distinct sound when approaching, that of a roaring freight train.
If a tornado comes skipping through your neighborhood, your first thought is to get to the center of the house. Stay away from all windows, doors, and outside walls. If a tornado strikes your home, it's may well blow the roof off the house and knock down the outside walls. Inside walls, such as those around a bathroom have the best chance of staying up. A basement or storm shelter would be the safest place you could go, but most houses in New Orleans don't have either of these.