Not sure about Xmas Eve hours, but any of these would be worth checking out:
Tin Angel is our favorite funky slow-food kinda place
Copper Onion is not quite as groovy as Tin Angel, but still way 'hound-worthy
Red Iguana offers up what is arguably the finest regional Mex for hundreds of miles in any direction
Mazza is our stellar outpost for Middle Eastern. Full bar at the 9th and 9th location
Gracie's, Poplar Street Pub and The Bayou are all popular bars. The Bayou is more beer-centric than the other two. As Xmas Eve falls on Saturday night I'm guessing most bars will be open normal hours, and many will have live music.