Ankh-Morpork is any large city though after Dodger I suspect Mr. Pratchett prefers London. Even so, he snatches references to other cities as he needs.
Omnia is late antiquity Christian Egypt, being a desert nation across the ocean from Ephebe and filled with fanatical monks. The actual ones from history were real trouble makers.
Borogravia probably is a Balkan nation, though its political situation mirrors the Prussia of Frederick the Great. Fred fought and won against nearly all the great powers in Europe but to the rank and file Prussian it was all quite tedious.
Genua I've always thought was a Renaissance Italian city state (Genua=Genoa) but statements here seem to indicate this was an error.