Digital output from one nano to digital input of another. Can I connect the digital out of one arduino to a digital input of another? To detect a high/low state...
One powered in one room on USB. The other in another room separate psu (connecting the grounds).
I know I can use tx/rx serial. But if the other way would work, less programming and 1 wire less..
Yes, you can. As you noted, you do need to connect the grounds of both Arduinos. 

For some extra protection you could put a resistor between the output and the input. For example a 1kOhm. That way, if you accidentally set both pins as outputs, or plug the wire in the incorrect pin, you won’t get a dead-short.