In our quest for good Tex-Mex locally, we've been to Apache twice -- so far -- and we intend to go back again. The first time we dined in the restaurant, and the second time we had take-out.
The restaurant itself is a sort of hole-in-the wall downtown across the street from the Galveston Historical Foundation. There's easy access for the lunch crowd from downtown, the Courthouse, and ANICO, and I imagine the lunch is the busiest time for Apache. We were there at dinner one early Friday evening, and we were the only customers -- a little odd, but very pleasant.
Now down to the good stuff: Apache has GREAT food at a reasonable price! You can have combination plates, or you can order a-la-carte pretty much what you want. Ask for a takeout menu to take home with you so you can call ahead for next time.