That’s the long-demolished Stuyvesant Apartments on East 18th Street, generally accepted as the first apartment house in New York. It was built in 1870, and there were plenty of multiple dwelling already around by then, so what does “first” mean, exactly? The Stuyvesant wasn’t a residential hotel (furnished, with services), it wasn’t a boarding house (furnished single rooms), and it wasn’t a tenement (with shared toilets). It was an apartment house in the modern sense, where tenants rented an unfurnished group of rooms, including kitchens and bathrooms, and provided for themselves in those spaces. The apartment layouts are not bad:
The rooms are small, but that’s hardly unique among NYC dwellings then or now. The biggest problem is one that was not fixed in the city until the 1901 “New Tenement Law”, and that’s having meaningful windows. The side courts are ten feet wide, which is big enough to get some fresh air but probably not much light and certainly no view. The center court is not much better. The rear yard is exactly 4 feet deep, which is ludicrously narrow; fortunately the rooms that have rear-yard-facing windows also have windows on the courts.