$100 or $150 for incidentals. You can get an "excella card" at any check cashing and put as much cash as you wish on it. You can later get that cash back via ATM. If you do not charge anything to the room. But you can pay the bill in cash anywhere I've ever been.  

I doubt that you are looking for short term (1-4 hour) places.  I am guessing that you are coming in from SF and looking for a place to settle in, feel secure, and host.  Nevertheless, the Liberty Inn over on the West Side is a short stay, no reservation needed kind of place.  There are a few other places like that throughout Manhattan but I don't know the names or if they still exist.  

For any major hotel, I think you need a CC even if you pay the bill at checkout in cash.  They want that CC just in case you break things or empty the minibar