Fountainebleau and Fairview-Riverside
Fountainebleu is beautiful but we actually like nearby Fairview-Riverside more. It is not on Lake Pontchartrain but on the Tchefuncte River in Mandeville. It is quieter but you do get to see some interesting river traffic. Just be careful not to go if there is a brisk south wind for a few days as you may get cut off in there by rising tides. It has a brand new bath house in the area by the river. You do not want to stay in the area by the ranger station, make sure you get in the river loop. Really nice sites.
We found Bayou Segnette too crowded and noisy and looked at St. Bernard and decided not to stay there. Too close to the city for us, I guess, although you can get to public transportation fairly easily from both. We actually like the trip across the Pontchartrain Causeway from Fountainebleu and Fairview-Riverside and you are fairly close to great dining and shopping from both. A couple off the wall places featured in Diners, Drive-ins and Dives from Food Network are close by.
Stay across the lake, go into town during the day (or night) then go back to the park to relax.