It really depends on the type of theatre that you are. If you are a professional company then the previous advice is spot on and you should go through your local LORT organization to find the awards. I will say, having been a judge for a regional theater award for three years, you likely will have to provide tickets to judges and meet strict eligibility criteria that may involve number of performances, artist compensation, years in existence, etc.
If you're a community theater there are often awards dedicated to those as well where the eligibility requirements may be a bit looser.
Based on you saying you're in New Braunfels, TX you'd probably want to touch base with the Alamo Theatre Arts Council (though you're officially out of their jurisdiction which is limited to Bexar County) or the San Antonio Theatre Coalition (SATCO).