I'm shocked that this one hasn't already been covered in Have You Played, given that it appears on our Best Management Games Ever list, but this does mean that I get to be the one writing it now. Zeus: Master of Olympus (frequently now bundled as Acropolis with its expansion Poseidon: Master of Atlantis) is, and will probably forever remain, one of my most treasured games, let alone the specifics of genre. It carries the perfect balance of beauty, difficulty, detail, and puns. They're Ancient Greek puns, too.
In Zeus your role is to build the great city states like Athens. This means you must not only contend with the usual headaches of city planning (fire, earthquakes, plague) but also some suitably Grecian ones (citizens like to have good access to theatres and philosophers), as well as the threats of myth made literal. These will often stand in the way of your victory goals. You need to mine a load of marble? Stick this hydra in your quarry and smoke it!
Usually, you have to summon heroes to dispatch said beasts, who have a set of extremely specific and often very funny requirements. Hercules demands excellent city wide gymnasium access and, if memory serves, loads of food in storage. You can also build massive temples to patron gods, who then turn up to swagger around your city and occasionally cast miracles. Athena loves olive trees. Hades brings you silver ore.
There are so many lovely details to notice in Zeus. The little tiled roofs of the houses, and the delivery men who complain about hauling cheese across the city, and the Olympics that you can send your athletes too - watching them strut across the map to the host city, excited to represent you... And it all looks lovely! Like spending several hours staring at a sun drenched afternoon. I really can't recommend it strongly enough.