I did a post on the difference between focal vision and peripheral vision. A tennis player will go in and out of these vision types througout the point and match.
It is important that when you are going to hit the ball that you dont drift into peripheral vision. Concentration is key for this. Using peripheral vision to hit a shot is a poor choice because it is weak in providing key information to the brain so it can bring the racquet to the ball. Usually mis-hits happen.
I agree with TennisDog, you will not be able to see the ball into the strings - it is a blur you will see. The main reason why tennis teaching pros say to watch the ball into the strings is to keep the head still just before contact, at contact, and through a small part of the followthrough.
Try to concentrate and practice with distractions around. This is a good way for you to discipline yourself in your ability to hold focal vision. Focal vision can be easily disrupted from your emotions (that is why staying calm and breathing right to control your heart rate is important), your senses, etc. Most tennis players are undiscplined in this area. Nervousness can also cause a tennis player to go in and out of focal vision too much and help cause errors or inconsistent play.
A coach friend of mine has made a CD on the Mental and Emotion aspects of the game and tips on how to correct this. Lots and lots of good tips for players to use. You might find a couple you like and incorporate that in your game. I will contact him to find out where you can get one.