It is illegal under the New York State and New York City Human Rights Laws for owners, supervisors, staff, employees, etc. of a public accommodation to discriminate against a person on the basis of sexual orientation. That is no doubt the law and no one will dispute that with you. The issue which you may want to discuss with an attorney are what possible damages you incurred as a result of this incident. Proving damages is a requisite element in these types of cases.
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Not so much money, but the NYC Commission on Human Rights, or the NYS Division of Human Rights will require the hotel to conduct training for all staff so it does not happen again. You can find out more info by contacting either agency. If you are only interested in money, it may not be worthwhile to file a charge. But if you want to help improve services in the City, I recommend that you take action.
You do not make it clear if you had checked in; or were you denied a room or other services; or is it where you were subjected to verbal slurs but not denied a room or services. While it is obvious that the use of the derogatory slur was discriminatory, the hotel [allegedly] took remedial action once they were advised of it. As a result, it is doubtful that you would receive an actual compensation, and nothing substantial even if you did. But reporting the incident was the absolute right thing to do. You can always file a complaint with the appropriate government agency but, again, it will be more helpful in preventing "discrimation" at that hotel in the future as compared to putting money in your pocket.