Tex-Mex conjunto and tejano are the Mexican-American musical hybrids that give the Texas music scene some of its uniqueness. But Tex-Mex conjunto grew as much out of the accordion as from the guitar. Texas has a lot of German influence, after all. Guitar (or, rather, the big Mexican 12-string, the baso sexto) and accordion are joined by drums and the string bass to round out the band. Narciso Martinez is considered the father of modern conjunto, and Leonardo "Flaco" Jimenez made it popular. The more dance and pop flavored tejano is also everywhere in Texas; the tragically short-lived Selena is its most famous artist.
Indeed, if Corpus Christi cuisine has a touch of Cajun flavor, the music scene is a little different. This is a center for tejano and conjunto music. That Tejano queen Selena was born here, recorded here, and eventually died here. The fans, and the city entire, still mourn her passing, but the tejano scene continues to thrive.
El Paso, like Corpus Christi, has some tejano and conjunto roots and some clubs have mariachi nights. The music scene is pretty diverse, with a lot of latin and latin-jazz, as well as hip hop, blues, and regular top-40 stuff. Flipping through the radio is good fun, also, especially if you're looking for lyrics to supplement your Spanish. Not all top-40 stuff is American top-40 stuff.
Laredo is another major center for tejano music, with healthy performances of conjunto besides. The music genres have been known to mix with each other.