I'm finding Russia and Kongo to be the easiest cultural victories (particularly if the other is not in the game). Greece is nice for early culture from combat and the half-price Acropolis is great, but the hill requirement is surprisingly limiting and getting a religion is iffy on deity without sacrificing early expansion.
Three things I'm finding that really need to be toned down a bit -
1) Triple tourism from relics. If you found your own religion, this is a no brainer. Even if you are terribly unfortunate and can't generate your own relics (no Nan Madol or Yerevan), you can always trade for relics (see #3). And if you are Kongo, a capitol filled with five relics is powerful all on it's own, but if you can get it to be the religion with triple relic bonuses, it's +120 tourism from 5 relics. I typically don't try to manage my religion as Kongo (I take whatever comes) except to prevent a religious victory, but the capitol is the one exception - I will manually spread the necessary religion to the capitol as soon as I can.
2) Artifacts being worth more tourism than Art. Sure, artifacts require additional production in the form of an archaeologist, but they are easy to obtain and easy to theme. I find myself building a single art museum for the civics inspiration and to stash art for trading (see #3), but I don't permanently keep art there (except possibly some sculpture as Kongo). As Kongo or England, artifacts are an even bigger no-brainer over art museums. Victoria gets the bigger archaeological museums and Kongo's artifact bonuses are
doubled with a themed museum, so +12 food, gold, hammers with a themed archaeological museum.
3) Trading great works with the AI. The AI values great works, but it seems to value them all equally and will trade 1 for 1. Need some relics to fill Kongo's capitol or all your temples? Trade art for relics. Out of space for relics? Trade art for books. It's currently easy to come out way ahead in these trades and you can target your trades with civs that aren't going to run up your required tourist numbers.
My recent cultural wins have all been very minimalistic - no wonders, very few different districts used, barely getting any broadcast centers built before I win, so music plays a very small part of the tourism I have at game end. If one manages to fend off aggressive neighbors, winning is a bit too easy and straight-forward, even at deity (Peter neatly solves getting a religion on deity and not trying for wonders solves the wonder race problem).