Hello neighbor :o)
My but the list for edibles here in N.O. is nearly endless!!! Ha!! I see you are into fig and citris, both are great (I'm a fig fan too ;o). In truth you will be mostly limited by avaliable growing space. Most tropicals will do well here till we get that real cold snap which happens ever few years. There are low chill fruiting varieties of the more temperate plants like apples and peaches.
One of the negatives about New Orleans is the alkaline soil so no blueberries (I love blueberries). Also some herbs won't work well for us mainly due to the high humidity creating mildew such as the monardas, bee balm. One other factor is the mild climate also grows bugs quite well ;o) Oh and forget the bunch grapes ... stick with muscadines. Hmmmm. Check out the LSU Ag site for all sorts of great ideas.
If you have an particular questions feel free to write. I'm heavy into the permaculture ideal and frankly if its edible I want it ;o) HA!!! Of course I do love dem flowers too ;o) I do have a yard full of plants down here in N.O. (I've a house ... and small yard! .... in Arabi) but my focus has been on the place I'm building up in Ms.
Oh and plug for Dan Gill's gardening show on WSMB 1350am. He is a LSU Ag professor in Hort. and knows his plants. His show airs Saturadys 9-11am.
Later Mike

Here is a link that might be useful: LSU Ag