Saw this on the new HotelsByDay website link when I put in for a search - this might find your needs perfectly ... on Broadway near the Union Square West area, easy to get to - plenty of upscale & cool places nearby to eat, free WiFi and microwave, etc. (no beds, didn't mention anything about access to showers ... places look cozy to sit back, relax, read & do some work) Best best - just $40 USD for 9 hours (9 am to 6 pm) plus any applicable taxes & fees, etc.
https://www.hotelsbyday.com/en/hotel..._asc&mode=city

Looks like the bed deal, there are day hotel listed tomorrow for locations in Manhattan, use the site above to search. No idea how this is but for so little, worth checking it out - looks more than those shared office rental w. reception desk - assumed that they can store/have a place to store luggage securely while you work and/or take a lunch break around the area, etc.