Ever since I was a little boy first learning the game, my dad would tell me to keep my head down but Jordan Spieth looks at the hole on his short putts. I personally look at the hole on all putts. Although I am not recommending this method for recreational players, I do recommend following the ball to the hole with your eyes. This will free up your putt stroke and not only create scary good distance control but amazing accuracy.
For the recreational golfer, I would suggest looking at the hole during your practice strokes to calibrate the proper distance and speed control as well as visualizing the putt. Then when making the actual putt stroke, follow the ball to the hole with your eyes.
When trying anything new with your putt stroke remember that success comes from trust and confidence. Ironically, trust and confidence comes from success. The more success you achieve with this new method the more you will begin to trust it and increase your confidence. There is no magic bullet or short cut for success so practice, practice, practice until your confidence creates trust and produces success.