***The main source
Ok, so you want to get a lot of raw culture and a lot of multipliers in three cities in a high difficulty game (Emperor, Immortal or Deity). Where will the raw culture come from?
Buildings? No. How many WW do you think you are going to build, being realistic. 1 early and 2 medieval, maybe? And smaller buildings add simply too little culture. There is a long way to 50000

. It would take too long.
(Note: BTS has many more interesting buildings and Sistine's add a great benefit to building temples and monasteries).
Specialists? No. Only 4 culture per artist. 6 if you build the Sistine's. Too slow.
GA? No. You are not going to get more than 20 GL in any game. At least if it doesn't go so late that Deity AI launches their Spaceship. 20*4000=80000, not bad, but you need another 70000 out of somewhere.
Cultural slider? Yes. Here is where culture lies. A city that has built his cottages around 1000BC and worked them will enjoy towns around 1000AD. Since the obvious civic to run is FS, every town is worth at least 7 commerce per turn, which will convert into 7 raw culture if the cultural slider is at 100%. A city can easily get 10 cottages, so we are talking about 70cpt in all three cities. That's superior to any other source.
Ok, so the most important contributor will be the commerce transformed into culture, the second more important contributor will be GAs generated by artists and buildings will add another bit. (In BTS there are many new WW and Sistine's has changed a lot, so the balance has changed a bit).
***Research
If you are planning to use 100% culture, you are forced to use 0% research. But you can't do that at the beggining of the game or you won't know how to build cottages. Another important thing to build is cathedrals, so you must reasearch as far as Music. Liberalism brings +100% culture to all cities and +2 commerce for towns and a free tech, which can be Nationalism for the Hermitage. PP is interesting only in some games. Radio, Biology etc are interesting but come too late, it is better not to research so far. So my advice is: stop research after Liberalism, Music and Drama.
So a cultural game has 2 phases,
- Phase1, research as fast as possible towards Liberalism.
- Phase2, set the research slider at 0% and the cultural slider as high as you can afford.
***Efficiency
The goal is 50000

in 3 of your cities. Getting culture in other cities different than the 3 soon-to-be-Legendary ones is useless.
You want to get your 3 cities to Legendary status in the same turn. Not doing so is inefficient. For example, getting a city to Legendary long after the other two results in 110000-90000-50000 culture in the end of the game. There are 100000 useless culture between the three cities. What's the point in accumulating all that culture? You have made your goal much more difficult than it was needed.
***The multipliers
In principle, you want as many religions as possible in your empire. If you have 9 or more cities, you will be able to build 9 temples of each religion and, accordingly, 3 cathedrals of every religion, one for each of your soon-to-be-Legendary cities. FS affects all of your cities just the same. But there is a single Hermitage. Where should you build it? Let's make it clear with 2 examples:
Example1: 9 cities, FS, 2 religions, 6 cathedrals built, your 3 cities are doing 150, 100 and 50 raw cpt, they have accumulated already 5000

each, you expect to get zero GAs in the course of the game.
Solution1: This is the worst possible situation. The Hermitage should go in the worst city. The Hermitage will contribute only 50cpt to your victory.
If we don't build the Hermitage, the cities will reach Legendary in 100, 150 and 300 turns respectively. If you built the Hermitage in the first or the second city, you will reach victory in 300 turns. If you build the Hermitage in the third city, you will reach victory in 225 turns ( (50000-5000)/(50*4) ).
Example2: 9 cities, FS, 2 religions, 6 cathedrals built, your 3 cities are doing 150, 100 and 50 raw cpt, they have accumulated already 5000

each, you expect to get 7 GAs in the course of the game.
Solution2: You must build the Hermitage in the second city. The Hermitage will contribute only 100cpt to your victory.
If you build the Hermitage in the first city, the best you can do with your GA is to bomb them 0-1-6, for your cities to reach Legendary in 75-137-140 turns. You win in 140 turns.
If you build the Hermitage in the third city, with the idea of helping the worst one as in example1, the best you can do with your GA is to bomb them 0-2-5, for your cities to reach Legendary in 100-124-125 turns. You win in 125 turns.
If you build the Hermitage in the second city, the best you can do with your GA is to bomb them 0-0-7, for your cities to reach Legendary in 100-113-114 turns. You win in 114 turns.
Are you wondering how I can calculate the best use of the GA so fast (1minute for all 3 examples and all possible GA distributions). Then don't miss the chapter on planning ahead.
Example3: 9 cities, FS, 2 religions, 6 cathedrals built, your 3 cities are doing 150, 100 and 50 raw cpt, they have accumulated already 5000

each, you expect to get 16 GAs in the course of the game.
Solution3: You must build the Hermitage in the first city. You are glad to do so, because that way the Hermitage will contribute the maximum, 150cpt to your victory.
By building the Hermitage in the first city and by bombing the GA 1-6-9, your cities to reach Legendary in 69-70-60 turns.
There is not better solution to the problem. Try it out.
What can one conclude from the study of the examples? You want to build the multipliers in the cities with the most raw culture, in order for them to be more useful. If you have enough GAs to bomb the worst cities and balance the finish dates, everything is perfect. If you are short of GA, you are forced to put the multipliers in non-optimal cities, cause you have not other way to balance the finish dates.
Another way of looking at it is this: the more GA you get, the most useful your culture multipliers will be.
Of course a real game is not as simple as this examples. The total number of GA you are going to get is not independent of the finish date, so iterative calculations are needed.
*** The best two strategies
The strategy I like the best involves building 6 (or 7) cities, cottaging 2 of them (the capital and another one), getting 3 or 4 religions, building the Hermitage in the best cottage city and cathedrals in the 2 cottage cities, using the main GPFarm as the third Legendary city, not building any cathedral there, bombing 9 or 10 GA into the GPFarm in order to get it to Legendary, using some more GA in the second city to balance its finish date with that of the first city, using any remaining GA into the city that will finish the latest.
Advantages: you don't need a lot of land. The culture from the GPFarm artists is not wasted.
The other great strategy involves building 9 (or 10) cities, cottaging 3 of them (the capital and another two), getting 3 or 4 religions, building the Hermitage in the best cottage city and cathedrals in the 3 cottage cities, bombing GAs in order to balance all three cities, using any remaining GA into the city that will finish the latest.
Advantages: you build as many cathedrals as you can. The raw culture of your worst city is better than the raw culture of the GPFarm.
Both strategies require a good main GPFarm and additional cities working as secondary GPFarms.