There is a listing at the SoLMSC Places to swim page for Isidore Newman School, but i'm not sure it is up to date.
try the love swimming link for more info. Ask them if they know of any other pools.
There used to be a pool at the JCC, at Jefferson & St Charles, just down the street from Newman. I understand Tulane University has a new pool, I would think that this is probably the nicest facility.
There used to be a pool at the Lee Circle YMCA, but i remember it as being pretty funky. There are probably other pools at various health clubs in the downtown area.
Elmwood Sharks is the most active USMS team in the NOLA area, but they are out in Metairie. Still, you may want to contact a representitive of that team, they may hae a better idea regarding pools in the NOLA area.