I would stay in one of the guest houses in the French Quarter. If yiu want upscale I would suggest the Cornstalk Inn. If you are on a budget, I would stay at the Frenchman.
The Frenchman has an "artsy" crowd, if that works for you. The Cornstalk Inn is more of a "Yuppie" crowd.
We stayed at the Wydham Riverfront. It is right in front of the Riverwalk mall which is where the ship docks. It is about 3 blocks from the French Quarter. Very safe - ask for river view and you can see the top of the ship when it pulls in. It was $109 a night on "www.nola.com" Some people got the W Hotel on Priceline pretty cheap and it is $250 or more a night. Also there is the Hilton in the Riverwalk mall. I don't know how safe it is since the barge hit it a couple of years ago and took out some rooms. Some of these have great internet deals on their own websites. Debbie