Another important thing to consider - people want to win. I want to get an advantage early, and build upon that to victory. I don't want to conquer my nearest neighbour and then squander in corruption and fail. Now, of course, you also want it to be balanced, so that there are decisions at play. Civ 4 did this in the great way - every city had a cost, that went up the more cities you have/the further away you are. So if you go on an rapid expansion through settlers or swordsmen too fast, your cities could essentially bankrupt you. But over time every city eventually can pay for itself.
But as well, you don't want things to be too easy. If I conquer my neighbour early, it shouldn't necessarily automatically mean that I win the game. Some other ideas to consider:
-When you go to war, it should cost money/science/faith/culture/etc... Maybe some, maybe all, maybe none. But I shouldn't be able to simply build an army, and send them off to fight a massive world war as everyone at home just sits around continuing on like normal. Now, maybe the cost is not a direct penalty, but comes in other forms. Sort of like the war weariness penalty to amenities that we have now, although it needs to be both obvious, yet fair.
-There needs to be an easier way for civs to catch up. Honestly it feels like every civ should have Russia's ability, where trade routes to more advanced civs yield science and culture.
-There needs to be more bonuses to be able to make friends with people. Especially with someone on the other side of the world, they really need to be more content by default. It always seems to me that everyone in the world is angry at me even if I've never attacked anyone. If you basically have no interaction with anyone else, they shouldn't really ever denounce you, which seems to keep feeding into a never-ending cycle of hatred. By default, people shouldn't really be upset at you unless if you do something to piss them off. Or would be awesome if it was more dynamic - so if you make a good trade with someone early, then they'll remember that, and just naturally veer towards being friends. Like in real life, you may not like everything your friend does, but unless if they do something that really pissed you off, you're probably going to stay friends through petty squabbles.
-There also needs to be more bonuses for staying friendly. Yes, you get more favorable luxury deals, and there's a handful of policy cards that can impact things. But as it stands, I rarely every have a reason to give into someone's demands. If they ask me to stop settling near them, most of the time, I find it doesn't really matter what I say to that, they'll just end up being angry with me later on. Maybe even if they could codify a nice system of bribes - like, I'll give you tea as long as you don't settle within 10 tiles of any of my cities. Or if traders and trading provided a better benefit for both sides, that would further encourage staying friends - if I'm getting +50 gpt by having traders going between lands, maybe I decide that's more valuable than invading.
-Which brings to another point - would be nice if there were more ways to basically play peacefully to win. Even stuff like bringing back the old allied victories like they've had in past games, that could be nice. Sometimes I do like going and invading the world, but sometimes it's fun to play the builder game and make my cities as strong as possible.