For a cultural victory, only build 1 city, then puppet the rest. It's impossible for a second city to produce 30% of the total cultural output of 10+ puppet cities and 5+ cultural city-states, plus the capital, especially if you capture a city that has a wonder (+100% culture output with the right SP).
Edit: Here's a quick breakdown.
Capital
1 for palace
2 for monument
3 for temple
5 for monastery
5 for opera house
5 for museum
8 for Stonehenge
4 for various wonders
+100% for hermitage
+100% for having a wonder
+33% for Sistine chapel
Total: 110 culture
Puppets
2 for monument
3 for temple
+33% for Sistine chapel
x10 for 10 cities
Total: 66.5 culture (assuming they never build opera houses, which they will eventually)
City-states
20 culture for industrial age ally
x 5 city-states on an average Standard size map
Total: 100 culture
Grand Total: 276.5 culture/turn
So a new city would have to generate 55.3 culture per turn on a standard size map in order to be a net positive
New City
2 for monument
3 for temple
5 for monastery
5 for opera house
5 for museum
+100% for a wonder
+33% for Sistine chapel
Total: 46.6 culture
Not good enough. This is also assuming you never build a landmark with your great artists which will add a total of 13.32 culture per landmark.