Some of the states that are reciprocity for California Cosmetology License include Oregon, Alaska and Alabama. The requirements for this are verification of licensure from Your Home State, preparation and testing. You need to check with your State's Licensing Board.
Call your State Board of Cosmetology. They may have a list, but it depends on which State you are interested in moving to. Some will accept reciprocity with a fee, some may also require you to take a State Law test also along with a fee.