Diplomacy. Go Siam, Venice, or Greece then down the patronage tree while focusing on making as much money as possible. Everytime a city state gives a quest for donating money or double money rewards do it. Try to save a up a big nest egg for the end game so when the world election rolls around you can buy every city state out and win.
I've honestly just ignored city-states, mostly because I've never really taken the time to figure out how they work.
They can give you so much. If you have a few militaristic city state friends you don't really need to build an army, a few actually will give you unique units like winged Hussars or conquistadors. If you run patronage they will give you science. And faith city states make getting a religion early game really easy. In my opinion unless they have a strategic position you should never conquer them
Sweet, thanks for the heads up. I'm probably going to start a new game tonight and go for culture/diplomacy.