The last time I stayed at that CY (also using a cert), I got a room where the window opened towards an internal corridor, which basically meant zero privacy if you opened the curtains. If you do choose that hotel, make sure you ask for an external view room.
That SHS is pretty nice, and if you don't want to walk the extra half mile, cabs in NOLA are cheap and plentiful. For a multi-night cat 4 stay with the spouse, that's probably what I'd choose.
At the cat 5 level, my picks would be the Ren Arts followed by the JW.