I spent my lunch hour researching Egyptian cities, and this is what I've managed to come up with: they should probably be in either Luxor or Cairo.

Luxor is older (it actually dates back to the ancient Egyptians, as opposed to Cairo, which is Roman, from circa 150 AD). Cairo is larger, has the museum and a distinct red-light district that would have been around in the '20's. Both cities seem to be fairly close to places of archaeological interest. Either city would work, though I'm leaning towards Cairo as the more probable. (Plus, Arthur could always work with the museum).