A somewhat "unique" item for central Texas may be Migas
(eggs scrambled with tortilla chips, hot peppers, onions, tomatoes, topped with cheese). I have heard the claim that they were "invented" at an Austin restaurant, but I don't know if that's true. Generally a breakfast item, many restaurants serve them any time of day.
Other foods around here that might be considered "best of" would include brisket, huevos rancheros, breakfast tacos, chicken-fried steak, and Tex-Mex in general. Because of the heavy Czech and German influences around the area, we have some wonderful sausages available.
(Did you ever consider that sausage may be the "universal" food
Seems like every place on earth has their own way of doing sausages, and everyone thinks theirs is the best.)
If you're ever down here in early summer, Texas Hill Country Peaches
(freestone) are about the best in the country. In late fall, Texas pecans are available and yummy.
Not a food item, but in March/April, the Bluebonnets
are in bloom along the highways and fields. Depending on prior rainfall, the thickness will vary, but on a good year, there is little on the earth that is as beautiful as a field of Bluebonnets. Like looking across a blue ocean...