1. What is the average board score for Neurology residency programs? Do I even have a shot with my scores?
~217. Definitely.
2. What can I do to improve my chances? Would it be a good idea for me to try to take Step 2 as soon as possible and hopefully, improve upon my Step 1 score?
Work with your neuro dept, get involved, demonstrate your interest. You should start browsing dept websites, most require that you have passed the step exam, others want scores atleast between 200-210. The step 2 doesn't mean much for M.D. students but not sure about D.O. students.
3. Does anyone know what are the good programs in California? Additionally, what programs (anywhere in the U.S.) do you think I have the best shot at?
Apply to all programs in Ca if that is where you want to be. It is a small cost considering it's importance. I doubt you will have any problems matching, but for some reason neuro seems to be getting more popular. 😀