ChelsE, I have put some time and hands-on research into this very topic.

Re: tonic - doesn't it come out of the fountain gun? Most every "mixer" would, except juices, red bull (I wouldn't get it if it's from a tap, though)...
I'm also dicey on all the "well" brands of *any* liquor - the generic stuff you get when you don't order a "call" liquor by brand (like Bacardi, or Cuervo, or Smirnoff). This is the equivalent of buying generic food - we wouldn't do that, and I doubt we should do this, because, who knows??? It takes a bite out of the wallet, but better that than my intestines!
(There's always (shhhhhh!!!!!!) THE FLASK OPTION!!!!!!

This is saving me money - but beware - you need to think ahead of time of exactly how much liquor is in there and how you need to measure and pace yourself so you don't overdo it. Seriously! (This threw me for a loop the first time!)
VODKA
GREYHOUND = gluten-free vodka and grapefruit juice = delish.
SCREWDRIVER = gluten-free vodka and orange juice = classic.
ON ROCKS IN A TALL GLASS + BOTTLED WATER (mix yourself, not from gun!) = actually nice, and hydrating!
I only do non-wheat vodkas myself and recommend that (I had bad experiences, don't care what the "official" word is). Lukosawa (potato), Chopin (potato), Ciroq (grape), Smirnoff (from what I've heard here, corn, but I've been too chicken to try yet) are the ones I know off the top of my head.
TEQUILA
MARGARITAS - Cuervo assures me they're gluten-free. So does Cointreau (they use no ingredients derived from any of the bad grains, unlike a lot of liquers). So I order margaritas with those, and I make sure there's no other baddy ingredients in there or stuff out of the fountain gun (the place I go to adds house-made lemon/limeade.)
SHOTS (of Cuervo or other call brand) - !cuidado!
RUM
Any CITRUS JUICE AND RUM (call brand) should be drinkable.
My friend Liza from Puerto Rico says *anything* goes well with rum, but I guess she's partial.)
Again, ON ROCKS IN A TALL GLASS w/LIME + BOTTLED WATER (mix yourself, not from gun!) is quite refreshing.
Again, I always order a brand I can expect to actually be made from sugarcane.
HARD CIDER IN A BOTTLE
sometimes hits the spot - I'm dicey on the ones on "tap" - bar rags may be used to wipe all the taps (including beer, pools of liquor, etc).
Have fun in Dallas!
Paula