You might want to hone your Google skills…
I just googled “hotels NYC minimum age 18”, and found several
hotels (e.g. the Hilton Times Square — and a few other
Hilton brands — and the Manhattan at Times Square) that have
a minimum age of 18.
Even better, I found a TripAdvisor post that lists nearly 150
hotels in New York that accept people under 21. This seems
like a common question there, just as it is here.
Call the hotels to confirm their policies.