I'm not an expert on NO either, but I've been there a handful of times.

Keep in mind that you are going for Mardi Gras - you will have to pay to go to the bathroom, you will have to wait in a long, long line for anything, and there is trash and puke up past your ankles. But have fun!

I second the New Orleans Cigar Factory - in addition to Decatur St., there is also a small one on Bourbon St. Check it out, some reasonably descent smokes. They roll fresh on Bourbon, too.

Enjoy beginets and cafe au lait at at Cafe du Monde (a tradition)
Enjoy Hurricanes and rowdy piano bar shinnanigans at Pat O'Brien's
There are great "Hand Grenades" (it's a drink) at Tropical Isle
Start the evening at Tipitinas

Practical advice for Mardi Gras parades:
The people down there won't pick up anything off of the ground for a REASON. Follow their etiquette.
But feel free to knock over grandmothers and little kids for beads and small doubloons. You'll get the idea quick.
Wear cargo pants or shorts to the parade. You can carry beer in the extra pockets. Or, better yet, bring a Camelbak full of (liquor of choice), and keep buying (mixer of choice)
Wear boots. While practically you might think this might clash with said wardrobe described above, you'll be wading through tons of garbage, such as beer bottles, vomit, and trash. Besides, you haven't seen the outfits worn there yet.

NO advice in general:
Things are pretty loose there, but general hygiene laws still apply. You can and will get nailed for peeing in the street.
If she's too easy and too pushy up front, she's a man.

Honestly, have a great time. Be safe. Travel in packs. Always know where your wallet is. But I've been going to Mardi Gras parades for 25+ years. I've been to New Orleans for Mardi Gras 3 times. I would not go back, but then again, I'm too old for that scene.