You can find Ohio high school playoff brackets at the website for the Ohio High School Athletic Association. Other sources include local newspapers and the schools' websites.
Other than the Ohio High School Athletic Association's website, the best online places to find Ohio high school playoff brackets are Cincinnati.com, Cleveland.com, Ohio.com and the national high school sports website MaxPreps.com.
Other sources of playoff brackets within the state are the websites for the Columbus Dispatch, WCPO and FOX19.
For basketball specifically, Prep Hoops Ohio is a good source of playoff brackets. JJHuddle.com also closely follows Ohio's high school sports, offering playoff and tournament brackets.