First off, the CVB's website is (not surprisingly) www.neworleanscvb.com
They're located on St. Charles between Josephine and St. Andrew towards the Garden District and are very helpful. We were staying in what is called the Warehouse/Arts District (and which, I'm told, was called the Red Light District ten or fifteen years ago) so we could walk most places. Parking looked to be very tight around the French Quarter; hell, driving was all but impossible there. It would stand to reason that the Harrah's Casino at the bottom of Canal St. would make parking relatively reasonable to get folks to come in and lose their shirts, but I can't guarantee this. There were massive parking lots at Riverwalk (mall) and you could catch the Riverfront trolley to more exciting parts.
This is a 192-page official guide to New Orleans, complete with index, and there's literally no mention of parking. If you do go to the Visitors' Bureau, slap them for me.
Here ya go; our hotel gave us a copy of these people's map. Unfortunately, it's a black-and-white copy of a color map, so the parking lots don't actually show up. PDF version here:
http://www.mapneworleans.com/secondarypages/mapsample.htmlHa! The Multicultural Guide brochure also has the same map. It appears that the largest lot is on Decatur St. at St. Louis in the French Quarter. Another map shows it all the way at the bottom of St. Louis; isn't this fun?
Take the kid to Mulate's, 201 Julia St, for cajun music, food and dancing. The best, the best, and the sweetest, respectively. (Lots of elderly people and little children participating in the latter.)
Hope some or any of this helps, and that you and the young one have a great time!