There are only a small handful of bars in the area by the stadium. For the most part it is mainly restaurants and a few shopping centers. There is a small bar called The Pump and two pool halls/bars right off 360 & 30. Best places are a few minutes down the road. Bentleys is an English style pub & J. Gilligans has good food/beer prices since they are right near UTA.
Everything is likely to be packed by the stadium. Lincoln Square is real close with lots of parking space & places to eat. Mostly they run shuttle trams for games, so I assume they will do the same for Mania. If you have transportation you can get away from most of the people and go somewhere by the Parks Mall or Arlington Highlands. They both have many restaurants/bars in or right near them. Just about a 10-15 minute drive from the stadium.
Best bet is to google some places and make reservations if possible. Traffic can be a bitch during games, so you can count on it being crazy for the show. Downtown Fort Worth & Dallas are bigger areas for the bar situation because where the stadiums are in Arlington is not a traditional downtown area like most cities. It is mainly restaurants, shopping centers and such within that mile or two radius. Six Flags and both stadiums are very close together and they rely on in house food/beverage sales so do a bit of planning if you want to escape the shit ton of people that will be flooding the immediate surrounding area.
When people come to visit, we hit the stadium or whatever and usually drive to downtown Fort Worth or hit a local spot like Gilligans. Just depends on where u are staying, but traffic going towards Dallas is going to be a bitch afterward cinsidering that is where many are going to go.