The best weather here is September - October and April - May. the worst months are August, hot, close to 100% humidity and no air moving and January, usually cold and rainy. There really is no off season. Mardi Gras and Jazzfest time are the big time events here. Also to be avoided unless you are interested are several special events which pretty much tie up the hotels and attractions. They are "Southern Decadence" - a festival of alternate lifestyles on Labor Day weekend, Essence Festival around the 4th of July, and several of the big football weekends.

As far as general weather conditions and travel - no where is good these days. A mountain goat falls off a cliff in Greece and air traffic is affected in Denver. And of course, we all know that the airlines blame everything on bad weather in Denver.

Re: some of the other places mentioned. Chicago is great. We used to go there in late May/ early June for CES convention and it was nice. Virginia and the Carolinas are also very attractive.
We used to go to Las Vegas in January for the CES show and I realy did not like it at all. I found it to be even more artificial than Disney and not at all a relaxing or interesting place to visit.