There are varying theories on where a batter should focus their eyes during an At-Bat. The hat. The jersey. Dead into the eyes of the pitcher. The truth of the matter is, it doesn't make as much difference where the batter looks while anticipating the pitch, as long as they are looking in the general upper body area of the pitcher. The more important matter is how they are looking.
Waiting for a pitcher to deliver a baseball is one of the most nerve racking things in sports. Aside from the danger of a dense object flying at high speeds toward you. It can be stressful being in the spotlight. All the fans focused on your ability to either hit the ball or strike out. You've got three cracks at it, but if you fail, take the walk of shame. The fact is even the best players in the world feel anxious in the batter's box.
Staying relaxed at the plate is very advantageous for a hitter, and this temperament goes beyond the body and mind, it includes the eyes. The best thing a hitter can do with their eyes as they await the next pitch is simply - relax. Consider a time you've taken part in a staring contest. The longer you focus in on an object, the more the eyes strain, and the more difficult it becomes to maintain that focal point. It's the same concept in batting.
A hitter's sights should be softly set on a pitcher's upper body until the moment of release. This approach will preserve the eye's ability to focus when it matters most. Finally, as the baseball leaves the pitcher's hand, a batter's eyes should calibrate in preparation for that split-second of undivided focus.