I'm planning to come to New Orleans the first week of April, when I devoutly hope there are no special events going on! There will be 3 of us coming, including an almost 6 year old, so I'm looking for good places to eat with a young child. She's eaten out a lot here in the Bay Area, so she's certainly used to going to restaurants. But she has a tough time waiting too long (so do we!). Uglesich's sounds fabulous, but I'm not sure she'd make it.
It would be nice to go (and thus take her) to one or two fancier dinners, but some upscale places tolerate kids and some don't. There are also some places that are just too hip for children, though that's rarer.
Locationally, we've got a reservation at the Hotel St. Pierre on Burgundy St. in the French Quarter. We weren't planning on renting a car because of the hassle and cost of driving and parking one there, but might be persuaded otherwise.
Incidentally, I think the cheerfulness to crankiness ratio on this board is really good.