Where in Egypt did Joseph and Mary travel when they left Bethlehem?

We do not know, but almost certainly they would have travelled from Bethlehem down to Gaza and then along the northern coast of the Sinai peninsula until they reached the Nile Delta. There was a road, together with inns and supplies of food and water by that route.

Any other route would have required considerable organisation, not only of supplies but also for security, as the Sinai desert was peopled by beduin who were not always well disposed towards travellers.