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Originally Posted by jordyn
Your only real recourse is to either ask AA again or sue in small claims court. They are obliged to provide "reasonable" hotel accommodations in this situation, so if this was the only option you'd have an argument that it is reasonable, especially given the advice of the AAgent. Whether or not it's worth your time to take them to court is a separate question, but given that you'd have been willing to sleep overnight in the airport as an alternative, it seems reasonable to think it might be.
Then again, as others suggest, going the voucher route minimizes your loss if you're likely to actually use it.
From Post #5:
"I was going to look into using my CC insurance. Not sure if it qualifies as an interruption or not since I made it to my destination and completed the trip."
If the OP's credit card has Trip Delay coverage, that insurance might well reimburse the difference between what the OP paid for lodging (and meals), and the $79 that AA has offered.