There's been a recent uptick in the number of concerts and sporting events I'm attending, which means I've spent more time than usual at arenas. Unfortunately, arenas are rarely good settings for gluten-free fare.
As always, what you can eat depends on the willingness of the staff to accommodate you and your judgment of if you think said staff will be able to get it right. Be attentive. Don't be afraid to ask questions. But if you know you're going to have a lot of questions, I recommend waiting to search for food until lines die down. The last thing you need are a bunch of rabid sports fans upset with you because you stand between them and their beer and hot dog.
So with the usual caveats about being careful, I recommend seeing if the concession stand can give you a 100% beef hotdog without a bun. No fillers = no problem! Explain that you have an allergy, aka that they can't just peel a lukewarm dog out of a bun -- it has to be a clean dog. They're usually able to wrap a naked dog in foil and send you on your way. If they don't have plastic forks and knives for you to use to devour with your dog, feel free to wander around to other stands. I've had to rely on spoons before from ice cream stands, but it isn't like I was cutting real meat. Or you could be manly and just eat the dog with your bare hands. I've done that before, too. Note that the "manly" option is not particularly attractive on dates. ...Unless you can eat a hotdog seductively in a stadium full of people? I dunno. Don't try it. Just eat your damn dog.
Aside from the bunless-wonders, there isn't much for glutards to eat at typical arenas. Some arenas will offer higher-end concession options like salads, chicken sandwiches, or ice cream, which may or may not be glutard friendly or adaptable. If they have fries, you could ask if they're cooked in the same oil as chicken strips, onion rings, etc. You could also ask about the nachos, but be warned that nachos are a real heartbreaker. If the squirty nacho cheese is safe, then the chips will be unsafe; if the chips are safe, then further inspection will reveal that the cheese is not. Hopes raised; hopes dashed. Maybe you'll have better luck than I've had, though. Hopes raised!
Otherwise you can drink a ton of soda and hope that fills you up. Spoiler alert: It probably won't. Or, and I am NOT advocating for this, you could try to stealthily sneak in a snack. This is probably against the rules, so don't do it unless you know the venue allows it. Or, even better, you could try to eat beforehand. Fill yourself up so you can sport out/rock out without having to worry about concession stand food. This last option gives you the extra advantage of not having to miss any of the game/concert waiting in line or reading ingredient lists.