A lot of things affect this, but the major ones are placing governors in cities where you've already built an allied democracy or oligarchy government. You need a core factional government if you want to place a governor there instead of recruiting a local governor/general and client ruler bodyguard unit from an allied vassal government building. This allows your settlement time to convert to your Hellenistic culture. Also, you should focus on building infrastructure that improves public order right away and build stuff that improves finances and population growth later on. As others have alluded here, there are also problems with certain cities in the Hellenistic Greek sphere, especially in mainland Greece, where certain cities have very poor public order if you do not construct an allied democracy or oligarchy.
If it really drives you nuts and you feel helpless about it, you can always reconquer those cities and enslave/exterminate the populace. If you're really desperate, you can also cheat!

You can decrease the population of any city this way, which usually undercuts unrest. Use this is a last resort, though, especially since recruiting a local client ruler usually solves the public order problem for a few decades, bringing stability and ensuring your culture spreads.
For the cheat, open up the console with the "~" button on your keyboard while staring at the campaign map. Type in the following, with the city of "Sparte" as an example, but any city, town, or nomadic camp can work with this cheat:
Code:
add_population "Sparte" -4000
Notice how there is a minus symbol "-" before the number 4000. You need that, otherwise you'll be adding people to your settlement. LOL. If the city has such a huge population that lowering taxes after that still doesn't help, just continue the cheat above, using the enter key in the console, until the settlement decides to be a good girl and behaves itself. Like everything in life, the game just needs a good spanking when it decides to throw a temper tantrum and defy you, its master, in your quest for fun and diversion.
