If yes, what is the statute?
If no, what could be some examples of claims and damages in the event of a hotel refusing someone under a certain age?
It is possible that this could fall under a breach of New York's housing discrimination laws, but I would not take the case.
This answer does not constitute legal advice and you should contact an attorney to confirm or research further any statements made in this answer. Any statements of fact or law I have made in this answer pertain solely to New York State and should not be relied upon in any way in any other jurisdiction.
Lawsuit / Dispute Attorney
What state? country? what age?
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Personal Injury Lawyer
Your post is unclear and incomplete. What "services were refused" ; how old is the "underaged person"; was that person seeking "services on his/her own, or with a parent , etc. The "damages" are what the underaged person is claiming to have suffered due to the "refusal" - which is not indicated in your post. Furthermore, it is generally required by law that a Minor (anyone under the age of 18, in most states) must commence and/or appear in a legal action through a Legal Guardian (typically a parent)- as a Minor is considered legally incompetent to commence an action on his/her own. Is a parent on board with your pursuit of legal action - especially since such suits can be expensive to litigate and somebody has to be responsible for the attorney's fees and other litigation expenses.
An alternative and much cheaper approach is to not give business to that hotel/motel ever again, and move onto more important things in life.
In general, age discrimination may be unlawful, including refusing to do business with someone based on age. But more information is needed to address your specific concern (if any).