Were there hotels in New York by the 1700s?

No, there were Inns and Taverns as well as "Houses of ill-repute" (prostitution.) However many of the older homes such as: Elfeth's Alley constructed in 1702 and the oldest continuously inhabited street in the U.S. 2 houses on the cobblestone street are open to the public .. the Museum House and the Chairmakers House. Many of the older homes from the 1700s have been kept in tip top shape and some are open for B & Bs.