U.S. citizens living outside of the U.S. should register and vote in the state and county where they last established residence (domicile) in the U.S. before moving outside of the country. This includes voters that no longer maintain a U.S. residence.
You do not need to have a U.S. mailing address or own property. It does not matter where your relatives live or where you spend vacations. Your state of voting is based on the last place you lived.
You will use the address of the last real home you had in the U.S.—where you actually resided. This is your "voting residence address," and it is this address that defines your state and jurisdiction for voting. You cannot use a P.O. Box as your last U.S. address.
If you are unsure of what address to use, you can see the question "What address should I use when registering to vote from overseas?"