For cultural, religions are your friend. Try someone who starts with mysticism and found Hindu and Judaism. Then use The Oracle to found Confucianism. Make sure those religions are founded in those cities you try to get to legendary. Your first great prophet can be settled to support early growth or can bulb you christianity or build a shrine. I do not recommend that. Better wait which religions spead on their own and build that shrine.
Use your first great scientists for philo.
spread all religions to your cities. cities that are not going to legendary build temples so you can build more cathedrals in your three big cities. get at least 8 cities (iirc for hughe maps) to build 2 cathedrals/ city. only occasionally build wonders.
the pyramids are great help (artists specialists produce beakers)
DONT miss the sistine
statue of zeus is useful if you have ivory
parthenon can be great
try a game with gandhi. he's spiritual and philosophical, probabely the best combo for culture. philo makes your GAs pop like there's no tomorrow and spiritual makes you switch without anarchy. keep in mind that religions present in a city create culture if you have no state religion (+1 for any religion, +5 for holy city). switch to a religion for happy caps. spiritual helps your diplomacy. someone comes asking to switch to his religion/fav civic? GREAT! free diplo - boni! You can switch back anyway soon without anarchy. diplomacy in culture games is very important as you won't build that many units in order to keep the culture slider as high as possible.
hth