Ziggurat Cities are the traction cities of Nuevo Maya. They are set out as ziggurats, similar to Aztec temples. They are never visited in the series, but they are mentioned several times and visited outside of of the series.
The Ziggurat Cities are seen as adventurous and even dangerous places. There are arenas in the ziggurat cities where prisoners are forced to fight each other and wild animals. Nabisco Shkin planned to sell the Lost Boys to fight in these arenas, but he never had a chance to do.
Tom Natsworthy and Hester Shaw visited the ziggurat cities between Mortal Engines and Predator's Gold in the Jenny Haniver to trade with them. Nimrod Pennyroyal has written a book on the ziggurat cities entitled Ziggurat Cities of the Serpent God. The book is much critisied by historians, and it is even rumored that he didn't go to Nuevo Maya at all, but had rather just been living in Barcelona with juggler named Concepción Zipsky. In the book he says that vampiric towns suck the resources from the ziggurat cities (though this is unlikely to be true).
They may appear in future works.