Bayou Signette SP is a really nice one. Our preferred when camping in NOLA. Short run into the city. Very well maintained and clean. Space between campsites. Very clean showerhouses. WiFi included.
Since you're interested in visiting the plantations then Bayou Signette makes sense. It's on the west edge of NOLA. The plantations are along the Mississippi River west and north of NOLA. Heading west from Bayou Signette you avoid the NOLA traffic. A few small towns along US 90 but it's a good road and traffic isn't bad. When you get on the river road (LA 18) you'll start getting to the plantations that are open for tours. Oak Alley west of Vacherie is probably the most famous as it's picture is most used for tourist advertisements. You'll recognize seeing the picture of the place from the river road looking up the walkway under the oaks. All the plantations are a little different due to when they were built and in full operation, who owned them at the time, and crops grown.
Rosedown Plantation at St Francisville is operated by the State of LA and is about a nice 3 hour drive from Bayou Signette. Very nice tour and not the crowds you can get at some of the plantations closer to NOLA. A nice side tour after leaving Rosedown is a bit further north to Angola Prison. They've got a very nice tour and museum. Lots of history. You don't enter the prison grounds and not likely you'll even see any of the prisoners. The tour is of the old part of the prison which includes the old execution chamber and all is outside the first gate. Well worth getting off the beaten path to visit.