Texas' most Instagrammed restaurant is called Social Junkie Sports Bar in Houston. I can think of quite a few great restaurants in San Antonio that should've been #1, but then, I'm pretty biased.
The good thing about this list is that it has the restaurants all the IGers are talking about, which will help out when you travel this summer! You obviously want to stop and eat somewhere that's getting lots of buzz. You know it'll be worth it.