So if you're going to get an Airbnb, look towards the south of campus. North of campus is all student housing and low income housing. Downtown might have a few spots and it's perfectly safe between the levee and I-110. Pulling this up from Airbnb:

All of these should be relatively fine. Downtown BR will have people staying in the hotels there. If you want to pick a good hotel, we stayed at the Watermark and it's awesome. Great bar, restaurant, and nice rooms. There's also a Hilton that's very nice. It's not a big downtown so you will not have a ton of options and can go through it pretty fast. The hotels listed by LaBR4 are all great, specifically the ones off campus.

This would be a 5 minute drive from campus and I believe there is still a bus system that works this route during game days. Other posters will be able to confirm this for. There are a few bars to visit. I believe Boudreaux & Thibodaux's will have reopened by then. Bengal Tap Room has a solid beer selection (with majority local brews) with decent food. River Room is a fun hole in the wall cocktail bar. The Vintage serves drinks day and night, but is mostly a small plate breakfast spot during the day. If you want local cuisine in downtown, closest will be Capital City Grill. There are better options close to campus that are worth a ride to (Parrain's, Mike Anderson's, and Chimes come to mind).

L'Auberge is about 10 minutes from campus and does offer a shuttle service as well. The ride back to the casino is not quick, but it's air conditioned and you can sit instead of having to drive through the mad traffic. Lots of food options there and a pool.

If you've never been to New Orleans, it's definitely worth exploring the French Quarter and Garden District on foot. Don't talk to people on the streets trying to sell you shite. If you get a car, expect to hit at least 5 potholes. Not an exaggeration. The roads in NOLA are absolutely jacked up.

Greyhound bus station is BR is sketchy but right next to downtown. You and your friend will be fine. You can honestly walk to downtown from the station, although I would suggest just catching an Uber or something out of there. I think FlixBus offers a service as well. They're fairly inexpensive.