Any of them in New Orleans
on the lake will be fine. SouthShore has the best liveaboard
facilities and is probably the easiest to get to the French Quarter from, but is located pretty far from everything else.
There are three other marinas
I would recommend first. The Orleans Marine
(also called the inner harbor), The New Orleans Municiple Yacht Harbor (the outer harbor), and bucktown marina.
The outer harbor still hasn't been fixed from Katrina so it doesn't have power, the slips are dangerous, and they have limited slips that can even be rented out. I would steal clear.
The inner harbor is really where you want to be. Good slips, power, water
, live aboard amenities, etc.
Bucktown is fine, and is pretty much brand new. The problem is that it's isolated from the marine
suppliers that the inner/outer marinas
are built around. I know nothing about it's facilities except that whatever it has is pretty much brand new.