Call company headquarters and do your best. If you went to small claims you'd have to sue the company in a small claims court where the company is geographically located. Either in NYC, or if they also are located where you live, you can try suing there. Sounds like you wouldn't be around NYC enough to be around for court dates in NYC.
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Gather your paperwork and make your case to the hotel's franchisee or, if that fails, to the president of the hotel chain by certified mail. You can also file a complaint with NYC Office of Consumer Affairs. It might help you to consult with a NY-based consumer rights attorney.
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If they won't voluntarily pay then you can sue in Small Claims Court.
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