What is the best physical location for a home thermostat. Does it matter that it is near a cold air return?

Definitely not near the cold air return for starters. Usually a good place would be not near a register of any kind and not where it would be near an entry door either.

According to how your home is laid out, if possible somewhere close to center of house,in a room that is most used and on a inside wall,not attached to an outside wall, I`ve found its much better to be at least 10 feet away from return but better to be close to the return than be close to a supply vent