Generally speaking, the zakah should be distributed in the country of the zakah itself unless there is a certain need outside the country to spend zakah there and at the same time there is sufficiency inside the country.
The European Council for Fatwa and Research states the following: The principle is that zakah should be disposed of in the country of the zakah itself, unless there is sufficiency or there is a well-determined need outside the country. This is the verdict of the majority of Shafi`is, Malikis, and Hanbalis in the light of the hadith of Mu`adh (may Allah be pleased with him), in which the Prophet (peace and blessings be upon him) is reported to have said, “Tell them that Allah has enjoined on them alms that will be taken from the rich among them and returned to the poor among them.” (Al-Bukhari and Muslim)

Also, the above ruling is based on the procedure followed during the era of the Rightly Guided Caliphs, when the zakah was given to the poor people of the country where the zakah was levied; because sending it outside the country would disagree with its objectives, the most important of which is bringing about sufficiency among the Muslims of a certain country.
Therefore, the Muslims on whose wealth zakah becomes incumbent and whose wealth is in the Western countries, should give some of their zakah to the Islamic institutions that are based on reviving the commitment to Islam, such as Islamic centers, mosques, da`wah institutions, and Islamic schools, and give some of their zakah to poorer countries until sufficiency is realized there.