I like Cuomo and I think hes handled this pretty well.
At minimum his press conferences have been really well done, he's able to put his own ego aside and deliver the facts. He sticks to what his plan is, why he's doing it, and the information its all based on. He speaks with empathy and responds to "gotcha" questions with poise. The only one who has really been able to get under his skin even a little through all this is Trump, but squabbles between Trump and governors was inevitable.
The nursing home thing isn't a good look though, feels like any other time he's pointed back to federal guidance he's been able to be pretty specific about it.