There are many great insurance companies with great rates out there. Also many that do not. Limiting yourself to Geico, State Farm and Progressive is like buying only Ray Samuels because you recognize the name, or McDonalds, or Applebees. Seek out those companies that are domiciled in the state in which you live and don't forget independent agents who have access to several markets, which may or may not offer a better value than the companies named.
Rates are like a roller coaster ride. Sometimes a company will be high. Other times low. Most of the time someplace in between. Good luck.