The Hilton Garden Inn is actually not at the airport, although it is in Kenner. There is a Hilton right at the airport and if you're staying there, you may look into catching the French Quarter shuttle at the airport, but I doubt you'd be saving much money over a cab. If you're at the Garden Inn, you'll be right near the Treasure Chest casino on Lake Pontchartrain, so you may be able to find a shuttle there.
Don't know about park and rides running over the weekend, but you can make your own, assuming you're not going to try to drive back through Kenner intoxicated (a bad idea anywhere but particularly so in Kenner).
If I were in your shoes, I would drive into town on I-10 East, park near City Park and take the streetcar to the Quarter. You could catch the streetcar ($1 a trip I think) at Esplanade and Wisner at the main entrance to City Park, which is where it will be easiest to park. It's about a 1/2 hour ride down Canal to the quarter. (The schedule is available at
New Orleans Regional Transit Authority : Route 47-48: Canal Streetcar, Saturday, Effective: 11-11-2007
You could also ride uptown and catch the streetcar at Napoleon and St. Charles, which is a very nice ride, but that area of town will be harder to reach from Kenner.
Using this map as a reference...
new orleans - Google Maps
Exit I-10 at Metairie Rd/City Park Ave and go west on City Park avenue. When City Park Ave. dead ends at N. Carrollton, you'll see the streetcar line directly in front of you. There's lots of parking around there.
Good luck, have fun and thanks for coming.