What's ideal size for a listening room?

Here is another good calculator. https://www.hunecke.de/en/calculators/room-eigenmodes.html

Basically it is whatever room the wife will allow me.

It should have a door that closes and locks.

Would either of the rooms have any kind of sound treatments? 

This question is too generic for any kind of specific answer(s).  For example, first and foremost, what type of sound system is being used?  Are the rooms in question strictly rectangular or do they have odd kitty-corners or odd shapes?   Doors, arches or other openings?  Acoustical properties (e.g.  Typical drywall construction?  Insulation?  Solid cement, wood or other type walls & ceilings?  Windows?  Curtains?  Drapes?  Etc.)?  All of these are factors.

If it's not too much of a PAIN, set up your rig in both and let your ears tell you which is best.  Generally, my guess is the room with the higher ceiling would be your best bet.