We stay at Bayou Signette State Park which is on the SW edge of the metro area. Rural setting, sites have a lot of space between them, water and electric connections, very good Wifi at every site. Very clean well maintained shower houses. The park is very well cared for and safe. From BSSP you're about a 10 minute drive into the French Quarter. It's easy to get to from I-10 by taking 310 to US 90. I don't remember the price. Something like $20/night. A real bargain for camping fee that close to a major city.
We have stayed at Fairview Riverside State Park in Madisonville on the north side of Lake Pontchartrain. A nice state park but the sites are a lot closer together than at BSSP. Fountainbleu SP is also on the north side in Mandeville. We stayed there once until we started staying at BSSP.
We also stayed at KOA West. Sites are very close together and tight. Others may like it but it's not the kind we prefer, particularly with such a nice park like BSSP available.
We stayed 1 time in another park in NOLA but I can't recall the name. Way too much city noise and traffic.
There's a couple of campgrounds next to each other in Slidel on 190 east of I-10 which aren't too bad. If it's been raining we found both of them to stand water in places.
Camped in every state