Which New York hotel did Tesla live in for many years before moving to the New Yorker?

Before moving to the Hotel New Yorker, Nikola Tesla lived for many years at New York City's Waldorf-Astoria.

Tesla moved into the Waldorf-Astoria around 1900, during the period when he was developing and promoting his wireless-power ideas. The hotel was then one of Manhattan's most prestigious landmarks, and Tesla's residence reflected both his fame and his connections with influential New Yorkers. His stay also became financially difficult: he accumulated a substantial unpaid bill and eventually used property connected with Wardenclyffe as security for debts.

Tesla's hotel history was more complicated than the question suggests. After leaving the Waldorf-Astoria, he stayed at several New York hotels, including the St. Regis, Hotel Pennsylvania, Hotel Governor Clinton, and Hotel Marguery. He moved into the Hotel New Yorker in 1934 and lived there until his death in 1943.

The New Yorker is therefore strongly associated with Tesla, but it was his final residence, not his long earlier home. The Waldorf-Astoria named in the answer refers to the original hotel at Fifth Avenue and 33rd Street, later demolished for the Empire State Building site.