This is where families spread out blankets on the neutral grounds and have picnics. People even bring out playpens to lay down the little ones when it's nap time. It's a time for families to relax and have a good time, catch some stuff, and enjoy the parades. If all you've ever heard about are the wild times your co-workers have had in the Quarter when they come to Mardi Gras, remember that there are a lot of family folks who are a good bit more subdued than that. Kids love parades.
Locals bring out ladders and attach seats to the top so the kids can sit up and get a good view.
Even if you don't have a ladder, put your kid on your shoulders and they'll be able to see the floats and catch the stuff. Buy 'em a bag of caramel corn from a vendor before the parade gets there, walk up and down the parade route a block or two and let them see all of the people. We're all acting like kids anyway, so the kids will fit right in. There are over half a million people on Canal Street alone on Mardi Gras. Don't ever take your eyes off of your child.