What is a good drill for testing my stroke and how well I can hit the centerline of the cue ball?
See “Fundamentals – Part I: MOFUDAT” (BD, September, 2008). It discusses the MOFUDAT drill (The “MOst Famous and Useful Drill of All Time”). A demonstration of the drill, along with additional useful information, can be found in these videos:
Here’s another good stroke drill, using two golf tees: