Ponchatrain Landing as mentioned can be dusty but is a very viable choice in the NO area. The shuttle is great. Takes you to the French Quarter and/or the WW II museum. Parking in NO close to the French Quarter is hard to find (depending on the time of year) and VERY expensive.
Was there last spring - early April and it rained 8 inches in one day. There was no mud, standing puddles for sure. So don't sweat the dry or wet conditions. Nice place to eat on-site but we only ate there once - the day we arrived. Spent to rest of the time sight seeing.
The French Quarter park is great for location. Did not stay there, but mixed opinions about safety. During the day I don't see a problem, later at night not so sure. But may be overly cautious. Most people say no issues, so if you want tp spend 100 bucks a night (don't remember the rates) go for it. Location is perfect for the French Quarter. If you only plan to spend a day in the French Quarter and most of the time other places around NO, then the location does not mean as much.