I wrote out this detailed answer, then realized I could not CITE how much each city increase the cost of social policies. I have not yet found it in either the Manual or the Civilpedia. The only reference I found quickly is that on duel maps the increase is 30%. Since we need to know for sure to properly answer this question, I've posted a new question on exactly that.
But, rather than not answer, I post this with the qualifier: this applies best to duel maps, until we know the numbers for larger maps.
There are two basic competing forces to your question: Socical Policies cost more for each city you control, but each city you control gains you more production/gold/science. So you're trying to balance. Where is the balance?
3 or 4 Cities
That's a pretty definite answer to what would usually get an "It depends!" answer. Why?
Because each city increases the cost of social policies by 30%, for your next city to be worth it, it needs to increase the cultural output of your civilization by more than 30%.
Now lets pretend every city in your empire is the same... they'll grow into having the same food, same gold, same science, same production, and, because of all that, the same culture as well. How much does each city improve your cultural output, eventually?
City | Culture | Change
2 | 2x | +100%
3 | 3x | +50%
4 | 4x | +33%
5 | 5x | +25%
6 | 6x | +20%
Now its not looking to good for cities 5 & 6 there. All
things cities being equal, they don't add at least 30% to your civilization's culture, not even considering culture that doesn't come from cities. (like from City-states)
But, of course, cities are not equal. If you've played any Civilization game for any amount of time, you know cities are not all equal, and you know which ones are better: the earlier cities. Exceptions do occur, but you try to build cities in the best spots first don't you? That makes city number 4 look not so good either, because if city 4 is off by just a little, its a loss.
Still, if city 4 is decent, even if its a net loss, it will still probably pull a lot of its own weight so as not to be too much of a loss, and it will be a win for production, gold, & science. So build it if you have a good spot, or don't if you're happy with 3 cities. And, of course, don't build city 4 if you are going for Bollywood.
Conquer Puppet Cities
Puppet cities do not add to the cost of Social Policies, but can still add culture, when they get around to producing such buildings. Easy win! Especially good for such things as +Culture/city/turn (social policy & France). Note however, you can not achieve Bollywood with puppet cities.
City States are your Cities you don't own
I risk sounding like a broken record mentioning city-states for a cultural victory again, but I like to think about city-states in a way that relates directly to this: Each city-state is an extra in your empire, that isn't in your empire. All the benefits, none of the (normal) costs. Make friends.