Which wall should I install a replacement thermostat on?
For a regular thermostat, you want to place it where it can accurately measure the temperature of the area you use the most. With the Nest, you have the additional functionality of the motion detector which allows Nest to reduce your heat when no one is home.

Thus, your last option, centrally in the family room, sounds best to me.

The second option is not clear with regard to the view of people using the family room. If that location only sees people entering the family room but not in the family room, that makes it hard for Nest to know there are people home if they go to the family room and stay there a long time.