New Orleans Fly Fishing

I think they catch Rios on fly in City Park lakes.

any lagoon in city park.....

also ponds/lagoons in bonne carre spillway...

If you're targeting freshwater species on light tackle and just looking to entertain yourself rather than put meat on the table so to speak. New Orleans city park is a good start, look on a map, scout some suitable locations and pound the banks. HWY 51 can hold some fish, you'll just have to move around till you find them. Might have to stick and move several times. Likewise with the bonnet carre spillway has some fish. Again, these spots tend to hold smaller fish in smaller quantities. Don't go expecting to fill an ice chest with lunkers, but you might catch some fresh fish for dinner (except City Park, just something about fishing in the inner city doesn't appeal to bringing those fish home)
You might also want to try the creeks in the river parishes on the north shore. There are some beautiful rivers over there with 2 hours or so of NOLA. I only know of a couple of put in points that others have shared with me. Not something I'd want to blast on the internet. Some folks put in many hours scouting online maps than driving around looking for put in points. If you want to put in the time and effort, you can do the same.
There is New Orleans Fly Fishers. Good group of guys, look them up. You might have more success with finding some more specific spots talking to someone face to face.