How do you balance Science and Culture?
In my current game on Prince I’m going for a science victory and I’m tied with 3 other civs. On the flip side, I’m one of the lowest producers of culture/ civics since I literally have no ways to produce culture. China is currently in the lead in culture and he beelined to Synthetic Technocracy while everyone else is in the industrial era for civics!
Honestly it’s either one or the other for me. Other districts beside campus and theater district are very important for me like commercial hub/ harbor and industrial zone.
How could I balance this so I’m not severely lacking science or culture?
As I see it in general, early science is to be wielded like a rapier – a light, quick, maneuverable weapon and able to hit with precision strikes your immediate and mid-term goals in a large wall of options. You are not to yearn for a machine gun at once to hit them all from the start, you're aiming for little birds first, the time for Big Bertha will come later. Culture, on the other hand, is that 18-wheeler big rig ensuring you're really moving when you get it going, but it needs to pick up speed to gain that unstoppable inertia, so better start early.
Don't be upset if you're lagging in science at first. Early on you only need some science to hit what you need first in your game - a growth tech, a luxury tech or a military tech to deal with close opposition. If you overdo science at the beginning, you'll be researching faster and with every new faster tech your districts will also become more expensive faster. If your early science overtakes your settling and growth of your cities, you'll only be slowing yourself in getting further districts - they will take more production to build. Build a couple of campus districts for the eureka, then you can make a pause with science - target your research more carefully and only place further campus districts to lock in their costs, but switch to build something else.
And on the contrary, you can't really overdo culture. The more of it early, the better. More culture early means you'll be moving faster through the civics tree and get to more advanced governments earlier, which will allow you to use more policy cards. It will also expand your territory faster, meaning you'll be spending less money for buying tiles. And you'll need to buy some tiles to preplace those districts in planned spots for good adjacency. Also, you'll be getting additional spy slots and start leveling them up earlier. It is not only Theatre districts that can bring you culture, certain pantheons and religion can bring a fair share as well.
Then, when the core of your cities have been settled and grew, when your culture truck is well rolling, you can chop in all those pre-placed campus districts with their buildings, put in science specialists and catapult yourself past everybody else, leaving them in the dust.
Somewhere in between culture building and finishing preplaced campus districts should come a few commercial hubs. Industrial zones can be postponed for later. As with campus, you can place them when you can, but finish building last.
So my view would be a bit of science first and all out culture with sprinkled in commercial and military if needed. If you play your diplomacy well, you won't need much military, though, and if you trade well, that will compensate for a bit later commercial hubs. Then all out science again and industry to consolidate your domination.
It is a juggling game, with changing priorities and a number of cases apart. General plans may be one thing, but the game may roll you some neighbour who will dictate otherwise. Start a game and get Pericles as a neigbour, for example. Or Peter. You'll still have to get enough culture to get to Political philosophy and Oligarchy quick enough, but the emphasis will be on science/military, to get better troops than them to take over their nice little empires with all those new and shiny theatre districts or holy sites for your own use, sparing you the effort of building them yourself.
Prince is forgiving enough difficulty, so you can experiment as much as you want.