If you are a U.S. citizen temporarily residing outside of the United States or a member of the Uniformed Services or one of their dependents, you are eligible to vote the entire ballot including local offices.
If you intend to live outside the United States for the long term and you aren't maintaining your domicile in your previous state of residence, under federal law you maintain the right to vote for federal offices (President, Vice President, U.S. Senator, and U.S. Representative). That federal law is called The Uniformed and Overseas Citizens Absentee Voting Act (UOCAVA).
For more details, you will need to check the laws of your state, which you can do so by going to the State Voting Requirements page, inputting your state, and looking under the “Eligibility Requirements” tab.