Port side for the first 1 - 2 hours. The French Quarter will be on the Port side. While docked at the port, the Starboard side will be facing the city for most of the ships I see docked. I pass over the bridge - port area everyday of the week. After this point just some small communities and oil refineries as you head down the river. I from a town about 1 hour south of New Orleans, a small fishing town called Empire.
Here is a post with some information on what can be seen.