How should he distribute the udhiyah meat when there are no poor Muslims in his city?

Firstly: 

The division of the udhiyah into three portions was narrated from some of the Sahaabah (may Allah be pleased with them), but the matter is broad in scope. What matters is that some of it should reach the poor and needy. 

Ibn ‘Umar (may Allah be pleased with him) said: With regard to the meat from the sacrificial animals, one third should be for your family, one third for yourself, and one third for the poor. 

Something similar was narrated from Ibn Mas‘ood (may Allah be pleased with him) 

Secondly: 

If the one who offers the sacrifice gives some of the meat to one poor Muslim, even if it is only one, after that he may give it in charity to non-Muslims too. 

Ibn Qudaamah (may Allah have mercy on him) said: It is permissible to give some of it – i.e., the udhiyah meat – to a disbeliever. This is the view of al-Hasan, Abu Thawr and ashaab ar-ra’y. That is because it is charity that is voluntarily given, so it is permissible to give it to a dhimmi (non-Muslim living under Muslim rule) and prisoners of war, as in the case of other kinds of voluntary charity. But in the case of obligatory charity, it is not acceptable to give it to a disbeliever, because it is obligatory charity and therefore is more akin to zakaah and kafaarat yamen (expiation for breaking an oath).

End quote from al-Mughni (11/109) 

Based on that, if you offer your sacrifice, then you should look for a poor Muslim and give him some of it, then whatever is left, if you eat from it, store it, give it as gifts or give it in charity, even to non-Muslims, perhaps that may soften their hearts towards Islam. 

If you do not know any poor people, and the Islamic centre can look for them on your behalf and give the sacrificial meat to them, then there is no reason why you should not give some of it to the Islamic centre, as you wish. 

And Allah knows best.