You're probably playing your game too unfocused. It's simple, at the settler difficulty, try to build nothing but things that would increase your culture and it'll come naturally. Don't try to do everything like conquering, teching, expanding all at once. Plus for culture you want to have few cities to not have your policy costs go far too high. 3-4 is a good number for standard size maps but you could probably go more at that difficulty.
Things that you want to emphasize on.
Buildings - Monument, Temple, Museum, Opera House, Radio Tower.
Wonders- Stonehenge, Oracle, Cristo Redentor, Sydney Opera House. Hermitage. Also wonders that give you more than one culture could be worth building.
Social Policies - Tradition for the Wonder building bonus, Piety for the Mandate of Heaven, Patronage if there's a good number of Cultural city states around, Freedom for the 100% cultural bonus with wonder in the city, also Free Speech for cheaper social policies. The last one is pretty much up to you. You could also get Rationalism instead of Piety if you are in the middle of a lot of grassland since you can get a lot of specialists running.
Techs - Calendar, Writing, Philosophy, Acoustics, Archeology, Telegraph, Radio, Globalization