The Arlington area is a little bit of dump, and other than six flags and Cowboy's Stadium, there isn't much to do in the area. Before the game, I highly recommend a tour of Cowboys Stadium and bring a football. Due to the stadium being artificial turf, they allow tourist to go on the field and play around, kick, pickup game, or whatever for as long as you want. If you decide to do this, I would call immediately for tickets because they will sell out.
Following the game, if you are looking for nightlife, I recommend going to Ft. Worth. Downtown Ft. Worth has some really cool bars, and are all within walking distance. Futhermore, the Ft. Worth Stockyards and Billy Bobs are also very fun with many country western bars and restaurants, and that is about a 3 minute drive from downtown.
Dallas, has many bars and restaurants as well, but Dallas is much more spread out, and everything isn't condensed into one place as well as it is in Ft. Worth.