Ole Miss @ Alabama seems likely to be the 2:30 game (and God I hope it is, because 2:30 in late September in BR is still brutally hot).

As others have said, The Chimes restaurant is virtually on campus and has your quintessential "Louisiana food"...poboys, gumbo, seafood, etc. Great beer selection. However, it can be very crowded on gameday, so arrive early.

Chimes is near the "North Gates" of campus. On the south side of Tiger Stadium is the original Walk On's. Basically the same type of food as the Chimes, but more of a sports bar atmosphere. There will probably be a tent set up in the parking lot for a party/live music after the game. You can walk to the stadium from (though it's a little bit of a hike). You can also park in the big grass lot outside of the restaurant if you get there early enough. For comparisons sake, Chimes parking is far more limited.

If I'm coming in to BR for the day of the game (even a night game) I would drive to Walk On's and park. I'm pretty sure they open in the A.M. on gameday. Go in, grab a seat, and have a bloody mary or a few a.m beers. If/when you decide to venture out on to campus to check out the tailgating you can do so without having to worry about parking (which can be a pain in the arse closer to game time). Basically use it more as your "home base".

Walk around the campus and find the big tailgate parties (generally around the RVs outside the south endzone. The folks there will haze you a bit as an opposing fan. Maybe bring some beer and offer it to them. They will decline the offer because they are very proud of their hospitality and food, and will soon offer you plenty of drinks and food if you're friendly, but at least you won't appear to be a moocher. Given Arkansas is the opponent, you will probably see several tailgates roasting a whole pig (known as a cochon-de-lait)

There are other good places to go in BR. But since you are driving in on gameday I would keep things pretty simple.