When a city reaches a certain size you can consider building a new City. A City has certain development space constraints and if you are just going to stick with one it will be difficult to improve your character.
In order to build up your dominance in game it is good to plan on when is the perfect time to build a new City to bring in more resources and population. But do not forget the amount of food, gold, and current population when building a City.
Upgrading the Pavillion increases the number of cities that you can build and own.