GREAT question slotty!
My older son (minor league pitcher) has what many have called a great changeup. He will throw it in any count (including 3-0) to any hitter. But that might not be the "best" answer.
I think its a great pitch in a 1-0, 2-1 and 2-0 count, IF...you have command of it. IMO, the best ones look like strikes (and look like fastballs...read that arm action looks like a fastball) out of the pitcher's hand, but drop down in the zone by the time they reach the batter. My son tells me if he throws it for a strikeout he will 'turn it over' (almost like a screwball) even more to get more downward action. He rarely leaves one 'up' in the hitter's zone.