The capital's location depends on 1) when it's founded and 2) the size of the country at that time. Depending on the time period, different kinds of transport technology might dictate different "centers." For example, before railroads become widespread, a capital close to the coast might be essential to maintain rapid contact with the outside world (US in Washington, Mexico, Europe). This might argue more for a detached foreign ministry HQ, perhaps.
Even when Austin was selected as the capital of Texas, it was by no means central to the entire state (which extended north to Colorado). It was central to major population centers, likely zones of conflict (the Mexican border and Indian country), and international shipping/communication (via rivers to the Gulf Coast).
El Paso is difficult to reach, due to the harsh terrain (West Texas desert) that surrounds it. Unless you dredged the Rio Grande and magically increased rainfall, the river wouldn't be navigable enough to afford easy access. At the time, El Paso would have been dangerously close to marauding Indians, if not similarly malefactious Mexicans; it would have been far from both Anglo settlements and Mexican ones.
Maybe something near Brownsville would work, if you have a strong Mexican sentiment in your expanded Texas, but probably something in what is today Texas would be most probable.