Many suggest that your wear it on your non-dominant arm. This goes back to when watches had a winding/adjustment mechanism accessible to your free hand.
However, if your power right, and finesse left — activites that require power are performed with the right hand and arm, and finesse with the left, then what's your non-dominant arm? Are you with me still? For what it's worth, I use both sides pretty evenly.
You should wear you watch on whichever wrist your comfortable with it on. Here's the catch though. If you wear your watch on the same side with which you write, not only does your wrist drag because of the band but the band could becomes damaged. So, what's the best wrist to wear your watch on? Wear it on the hand you do not write with.