I want to sacrifice a sheep for ‘Eid. Should I sacrifice it where I live or back home?

The sacrifice is offered as a Sunnah by those who are not performing the pilgrimage. They are recommended to give a third of it to the poor, a third to neighbors and relatives and keep a third for their family.
As such, it is better a make the sacrifice where one actually lives. However, if one works in a country like Saudi Arabia, while people in his own hometown are generally poorer, then it is perfectly appropriate to ask someone there to make the sacrifice on one's behalf. Its purpose may be better served this way.
And God the Almighty knows best.