Florida: unilaterally fills state supreme court vacancies + can pick their LG + a lot of unilateral authority over county officials + extensive emergency powers invoked almost annually due to hurricanes
Actually, the Governor of Florida gets to unilaterally pick but only from a selection chosen by the Judicial Nominating Commission; basically, akin to the federal prism, the JNC is the President who nominates while the Governor is the Senate which confirms.
However, the JNC is largely appointed by the Governor (& unilaterally so, at that), & though the remaining members are appointed by the Florida Bar, the Governor has a veto over their nominees, so in practice, the JNC will never offer up a slate of nominees that a Governor won't be inclined to select from.