Texas has a rich music heritage, blues, jazz, folk, tex-mex, singer-songwriter, rock, psych, punk and on.
In addition to 13th Floor Elevators, I found Shiva's Headband worth a listen. Blues greats Texas Alexander, Lightnin' Hopkins, Juke Boy Bonner, Mance Lipscomb come to mind. Townes Van Zandt, Guy Clark, Nanci Griffith, myriad others.