Hmmmm..... Are we discussing Mexican food or Tex-Mex? Two very different types of food. Sure, if you want "Tex-Mex" then Texas is the obvious choice, but if you want authentic "Mexican food" then your choices in the US are very limited. I haven't been to the OP's Pepper's in Fernadina so I can't comment on its authenticity but having lived in Mexico for the last 15+ years I would definitely be qualified to judge whether it is or isn't authentic Mexican food. Just Sayin'
BTW, the fajitas in the photos looks deli!