The Lt. Governor.
This depends on the laws in the specific state. It might be the State Attorney General, Secretary of State, the Treasurer, the Speaker of the State House of Representatives.
It depends on the wording of your state constitution. The next person in the line of succession may be different from one state to another.
It is an elective office, so it remains vacant until the next statewide general election.
Then Lieutenant Govermor.