Keeping the tradition alive here in Austin, Texas. Blue Moon Bar & Grill (formerly located downtown on 6th street) has created a comfortable and intimate environment for some of the most talented local musicians to be heard live on stage. Blue Moon Bar & Grill offers a full service restaurant and bar in an upscale atmosphere. Planning a trip to Austin? Being located within the Best Western Plus / Austin City Hotel also creates an excellent opportunity to experience Austin without having to venture too far away.