first there really isn't a "season" here - we're on pretty much all year. I live on the east end of the MS coast, a little less than 2 hours from the city. There is at least one club in N.O., the crescent city cyclist www.crescentcitycyclist.org
there is also a club in Baton Rouge (about an hour to the west of N.O.). We also have a club on the coast, www.gulfcoastbicycleclub.com
. There are some pretty descent country roads over here and a pretty good group of riders. Depending on where you work you may be better off on the north shore (Mandeville, Covington, Slidell) and commuting into the city or maybe in MS, but that will be a pretty long commute.
Another thing - other than bridges - there are no hills down here. What part of the city will you be working in? Where are you moving from? It's not the most cycling friendly atmoshpere here, but it is bearable.