St Bernard is an OK state park. There's a bit of traffic at times getting to it as you're going on city streets.
We normally stay at Bayou Signette SP which is more on the west side of town. Going to it from the west involves very little town driving and those are small towns. It might not be as convienent for you.
Louisiana does a very good job on the state parks. Clean shower houses, electric and good wifi. Sewer dumps in the campground. Needless to say for that area of LA, the sites are level and flat.
If you only plan on going into the city a couple of times and visiting other places during the week you might consider either Fountainbleu SP or Fairview Riverside SP. Either are nice and we've stayed several times at them. They're not far apart from each other located in Madisonville and Mandeville on the north shore of Lake Ponchartrain. Easy to get to from I-12. Fairview Riverside SP isn't as large as Fountainbleu SP but bikes can be fun at either. Can't recall if kayaking at Fountainbleu but there is a boat ramp at Fairview Riverside if you want to give it a try. Alligators need to eat too.
Lots of good restaurants on the north shore. Our favorite is Morton's in Mandeville. Also The Chimes in Covington. Both have really good seafood. A $10 shrimp poboy served with fries and come hungry. They don't skimp on the shrimp.
Staying on the northshore and driving into the French Quarter can be a treat for the kids crossing the Causeway. $5 going south, no cost going north.
Getting into the French Quarter isn't too bad. I-10 to I-610 to the Elysian Fields Exit. Take Elysian Fields south to where you can't go any further and you're at the river 1 block from the French Quarter and French Market. If you turn right you'll be on Decatur St. Several large parking lots after you pass Jackson Square.
In the FQ for a lot of food and a good price we like Deanies. They have a Deanies in the French Quarter and one on the lake shore in the Bucktown area. Come hungry.
For plantation tours it depends on what you want to see. A number of them west of town. Oak Alley is probably the most famous and the one you see the picture of the most. They're all different and have different histories. For a plantation close to New Orleans there's Destrehan almost at the base of the I-310 bridge.
If you plan to go to the National WWII Museum then go as soon as they open and plan to stay all day.
If you want to ride the streetcar (trolley) then do the Green Line that runs from Canal St along St Charles. It goes past some really nice, big, old homes.
The Natchez riverboat runs 3 times a day. A nice cruise down the river and they explain some of the history. They also serve food on the Natchez but I recommend you pass. It's OK, not the best, and there are so many really good places to eat in the city that you don't want to fill up on what they serve on the boat.
Walk the streets and people watch. Lots of good street entertainment. Look for some good street music on Royal.
Watch out for the panhandlers. Watch your wallet and purse. If someone tells you they know where you got your shoes, keep on walking.