Yeah Arkansas is different than most states since basically the whole state only follows one team but it seems like fans are getting tired of "neutral" site games in college football as a whole.
I would probably go with either Farrell's, Foghorns, or JJ's Grill for places to watch a game. A lot of the bars on Dickson don't really get hopping until after 9 when the college students really get out. Yeehawg is one I used to frequent since there are several food trucks nearby but they don't have many TVs and it's a bit cramped for game watching.
For spots near the football stadium, Razorback Gardens is usually pretty popular for tailgating - it's a little further south across from Bud Walton Arena. There are some spots in Victory Village by the Greek houses directly across the road from the stadium but I believe those you have to pay for. Honestly it's been a while since I've actually tailgated though!