Alexandria was one of the major cities of the Roman empire, and one that would have appealed to Julian. It was founded by Alexander the Great, who was one of Julian's heroes. It was also the centre of a major pagan cult, that of Serapis. (If you are wondering who Serapis was, he was created by the Greek founders of Alexandria as an amalgam of Greek and Egyptian elements so as to appeal to both ethnic groups. Cynical manipulation of religion for political purposes has a long history.) And the intellectual achievements of the Alexandrians rivaled those of Athens. Basically it was his kind of place, or rather it would have been had it not also been an important centre of Christian thought as well.