The further apart they are, the more difficult they are to defend and administer at this stage. Every city should be churning out settlers. After you have built as many cities as your corner of the island will hold, turn the settlers to irrigating and building roads. All throughout this time, you have been gaining techs as fast as possible. As soon as you get the republic, start a revolution and change over to a republican government.
Cities operate much better under republics than they do under despotisms.
When you get democracy, you are equipped to go into the Second Expansion phase. When you do this, all cities will immediately begin celebrating, and will grow at a rate of one person per turn as long as there is surplus food. This places you in the Second Expansion phase. If you have done some exploring, and are not immediately threatened by another player, it can be a good idea to keep science at maximum until techs start to take too long to generate. Now is the time to develop industrialization, and military technologies.