Babylon:
The 2nd and 3rd goals (make Babylon the most populous city, make Babylon the most cultured city) can easily be combined into a single goal: Make Babylon the world's largest and most cultured city in 850 BC.
This leaves us room for a third, more ambitious goal, "Babylonian Captivity: Control two cities on the Mediterranean" (Jerusalem and Sur).
Korea: My issue with the Korean goals is that 2 of the 3 of them, build a Buddhist and Confucian cathedral and be the first to research printing, are essentially just mini versions of the Chinese goals (build 4 cathedrals and be the first to research 4 technologies, including printing). I like historical goals that are unique for every nation, so to that end, I propose two new historical goals for Korea:
- Settle three different great people in your cities by 1200 AD
- Construct Cheomseongdae by 700 AD
Also, I'm not sure if a Korean Great Prophet can use his "Great Mission" to spread Confucianism in Korea, but if not, that should be allowed. As Korea gameplay stands currently, you not only need to conquer a city with Confucianism in it in order to spread it back to your core cities to build Cheomseongdae, you also need to control two cities outside the peninsula in order to construct your cathedrals. I think my proposed changes would create a more historically accurate Korean game, while maintaining a challenge. The "Sink 20 ships" goal is fine.
Byzantium:
There was talk in this thread about removing goals that require the player to stockpile gold, because that can be boring. Personally, I don't mind these goals, and my Byzantium game was interesting, as I used my Great non-merchant-People to bulb new technologies while I kept my research at 0% to stockpile gold. I did remember Constantinople spent most of my Byzantine game building the Theodesian Walls and the Hagia Sophia, as that city has relatively poor

. So here is my idea:
Change the first historical goal from "Have 5000

in 1000 AD" to "Construct the Hagia Sophia, Theodesian Walls, and Mount Athos by 1000 AD". Byzantiums unique power is changed to "Crossroads of the World: For every 1000

in the treasury, your capital receives +10%

" (alternatively, +20% wonder production). This way, the player is still incentivized to stockpile gold to a certain extent, but the player can decide how much they want to spend on boosting

vs researching more technologies.
Indonesia:
I'm still playing through this civilization, so I don't have any strong recommendations. But personally, I feel that two population goals, with the final one being so far ahead from the 2nd goal (1500 to 1940) isn't great. Especially because, unlike military, infrastructure, or technology goals, controlling 11% of the worlds population doesn't really require proactive gameplay, it just requires a lot of "End Turn". I'm with 1SDAN about changing the goal to involve something about converting to Islam.