Not Always Possible nor Wanted
Some hotels, motels, health clubs, spas and even hospitals do still have in house laundries, but they are becoming far and few between, espeiclaly within Manhattan.
First there are the various rules,laws, regulations, and instructions regarding certain types of laundry such as hospital linen, that increase cost of processing. Then you have to figure the major expenses of labour (NYC is a union town),equipment, water, sewage, space for the laundry that could be turned into something else which generates profits and so forth.
According to the guy who runs our local laundromat, every other day or so several "Hispanic" women show up with huge bags of linen from a local hotel. They stay for hours using his equipment to wash and dry the linens. Mind you this place only has one 50lb machine, the rest of the front loaders are mid to small sizes, and none of his dryers are rated to even hold 50lbs or wash. More often than not the linens are crammed into whatever washer that will fit, over dosed with detergent, and how they come out is of no difference, off to teh dryers they go.
Either this hotel is sending housekeeping staff (unlikely) to spend hours doing the laundry, or some enterprising women have offered their services. Either way I wouldn't want to sleep on those sheets.
Laundry equipment is expensive, and the best use for any commercial laundry system is to keep them turning as many times per day. When you add up the costs of installing, maintaining, staffing, compliance and so forth with having an in house laundry, it often is cheaper to send things out. Especially when you have "bottom feeding" wholesale laundries that charge dirt cheap rates by the pound (to keep their own equipment and staff working 24/7 and cover costs).
Because Manhattan is an island, and rather densely populated, many large commercial laundries were and still are located either in Queens or Brooklyn (close to Manhattan) or even New Jersey. Much of this has to do with rules and laws regarding steam boilers which in the early days provided the heat and other power for large laundries.