Cultural wins are fine and do not always require alot of wonder although they help. My views on a cultural win
1) You need to decide fairly early (BC early) if you want to go for a cultural victory.
2) You need numerous religions, although founding them or even switching out of no state religion are optional.
3) Build temples and spread the religions to all your cities. Build monestaries as early as possible, especially in the three legondary cities. Build catherdrals for each religion in each legendary city.
4) Make sure you have a high production fourth city for military.
5) Build alot of cottages in your big three cities. When you rev the culture slider up late in the game, you will be amazed at the extra culture.
6) Make sure one of the legendary cities has unchopped or lumbermilled forrests so you built the national park there for the extra artists.
7) Make sure one of the cities has the globetheater for the extra artists while in emancipation.
8) Speaking of emanciaption, do not hesitate to switch to caste system once you rev the cutlure slider up. You'll have alot of happiness.
9) Beeline industrialization before radio. Tanks will protect you from the AI trying to take out one of the legendary cities.
10) Wonders are helpful, but not essential: Some that are more important than others: Parthenon, Sisten Chapel (the most important), Statue of Zues, SOL, The radio/Mass media wonders.
11) Do not ignore science or teching.
12) Get music and Drama early. Building theaters by 1 AD in the three cities gets them to +6 culture after 1000 AD.
13) Save GPs for the culture producing Corps (Sids, creative construction, Jewelers). They can be founded in a non-big three city, just make sure you have wall street there.
14) Keep the military and navy very high.
15) The eifel tower is useless except for some extra culture in the city built. Broadcast towers are cheap enough and you only need three.
16) Once you have teched Mass Media and Industrialization, ramp the culture slider to 100%. Build wealth in otehr cities if you need the money.
17) If you have not realized you should be pumping out great artists, preferable in one of the big three cities by running excess artists. Do not unlease the culture bombs until you know which of the cities will need them the most.
Not all above have to be in each game, but I tried to cover as much as possible.