BBQ - go to Cattleack if you can go for lunch on Friday - their beef rib is amazing; Terry Black's in Dallas, Hurtado's in Arlington, and Panther City in Ft Worth are our other favorites.
Tex Mex - close to grapevine are Mi Cocina or Muchacho; Joe T Garcia's in Ft. Worth is a classic place near the Stockyards (cash only so you can say you supported money laundering).
Best thing about the fair is the fair food - eat until you're sick.