Assuming you mean the Dallas Convention Center, I'm not real familiar with what all is around there. I'm told that the ginger man is a fine place for both food and suds, having a HUGE selection of fine beers on tap. http://www.gingermanpub.com/
There are lots of restaurants in the West End district, which is close to the convention center. Might have some bands playing out in the open there this weekend as well.