Which responsibilities are typically handled by local governments, not by state governments

As established by the U.S., Constitution, and given the division of government into federal, state and local levels, it has also been established that local governments, under the jurisdiction and observation of the state government, are responsible for certain acitivities such as plannification and payment of new roads, maintenance of old road systems within their jurisdiction, organizing and maintaining fire and police services, defining zoning plans and regulations and they can also regulate elections for their residents. These are all activities that become the responsibility of the two types of local governments: territorial, such as districts, and corporate governments, such as charters. This does not mean that local governments are totally independent entities; in fact, they very much depend on the state government, as a state government oversees the actions taken by local governments, and they may even go so far as to abolish a regulation, or an action taken by a local government if it goes against state law. The states may also abolish a local government and replace it, if this last one is not fulfilling its duties as established by state rules.

its d i know cause i've been googling it