I've always wished this, but basically no place, just mud, mud and more mud, unless far offshore, & this is from a LA native and a long term diver.
On occasion a couple of the N. LA lakes such a D'Arbonne and Toledo Bend, can be 5' feet in vis. if you like stumps, this is your place. Years ago some guys would dive in Black Bayou near Monroe, plenty o' gators now and another stump heaven.
I've never seen Ponchartrain very clear, but it has no significant relation to the River, other than the industrial canal with its locks, lake and river are not the same level, the water quality is much improved over the years, but for diving, nope. The offshore MS islands can be pretty clear sometimes, but the bottom is goop out there until you get way off-shore. Time is easier and better spent in the car back to Florida. Unless you want to do rig stuff.