Short Answer

Yes. However, if there are people more in need abroad, one may dispense their zakat abroad as well.

‍

Long Answer

Yes, according to many scholars, it is recommended to give Zakat locally. This is based on the instruction of the Prophet Muhammad (peace be upon him) to his companion Mu'adh, who was sent to spread the message of Islam in Yemen, that Zakat should be taken from the rich and given to the poor in their own community. By giving Zakat locally, we can better understand the needs and context of our own community and help those who are most in need. However, if there are people who are more in need outside of one's locality, one may give their zakat to them as well.