I only play at Prince, but I'm very near to moving up to Monarch. Is the decision to move a settler dependent on level? I've never moved the settler in any of my games (well, maybe once when I started on a flood plain and could move 1 space to a river plain and still settle-avoids the unhealthiness).
Settling in place seems to be the best idea because each turn you are out, the AI is busy researching techs.