There is something happening in New Orleans all the time, so your best bet is to avoid the biggest holiday/festival times. Those would include the end of Carnival, French Quarter Festival, Jazz Fest, Halloween, St. Patrick's Day, etc. The nicest times -- outside of those -- are March through early May, and late September through early November.

In terms of traditional NOLA dining, brunch at Commander's Palace is a must (much better than Brennan's, IMHO, and the Court of Two Sisters is not on my list of recommendations). The classic trio of Arnaud's, Antoine's and Galatoire's will check the box as well. Cochon is a must for Cajun, and John Besh's flagship, August, is special occasion splurge (though they offer a bargain lunch some days). But the NOLA dining scene is ever-evolving, and puts new spins on old-style dining; it's worth getting out of the French Quarter. The NO forum on Chowhound.com is a tremendous resource. My personal favorite restaurant is Coquette, in the Garden District.