I would like to see the ability to designate a percent of my gpt to more spies, science or whatever like in 4. I would also like a truly dynamic espionage, meaning I could destroy buildings in other cities, set back production, poison water/food supplies. The system we have now is utterly useless. The only thing you can do is steal tech and learn about other civs, yawn. I want to be able to affect what they do.
Better aviation. Right now you basically bomb cities or wait for bombers to come after you, again boring. Give us the ability to do air supremacy, no fly zones, that type of thing. Anyone ever notice when using a stealth bomber, there is no "stealth" to it. As soon as it gets close to a city, the city fires away. The whole point of stealth is to be invisible until AFTER you attack. Right now aviation is a one trick pony in my book.
More buildings, there needs to be a wider variety of stuff to build. Sure there is plenty to keep most busy now, but I often times run out of buildings to construct. Make the extra resources we aren't using contribute to something. Make things like cotton, wine and others good for something other than trading away or minor happiness upgrades.
Tech - There needs to be a revamp of the late game tech. Before you get to the modern age, you have basically everything you need to win. Make the last 2 eras count, make the units/buildings a significant upgrade over the previous era.
Give the AI a reason to really use a navy, not just spam units.
Cities -- Let's be realistic, why give cities the ability to place workers 3 tiles out from the city, just to have the AI spam cities that NEVER make use of this? Force the AI to either spread cities farther apart, or penalize them for spamming cities so close together (maybe a disease ridden water supply affecting multiple cities). It's just stupid to add a mechanic to use 3 tiles away from the city, then never use it.
City states -- Give the CS the ability to join your empire if your culture and happiness and a few other factors are high enough. Similar to how cities would "flip" in 4. They wouldn't just do it, they would prompt you to agree or not to let them join. If you don't want them to join, maybe they could become a player owned territory state. You could control some functions of the city, but not everything.
Workers -- Let's give them more to do. Each era should give some kind of improvement to the base improvements they start with. There is no reason a farm should give the same basic bonuses on turn 1 as it does on turn 1,000. Haven't we learned how to better farm since the 1600's? Let's use that kind of logic.
Why is railroad the best route upgrade we can build? Why can't we have highways/interstates or something beyond mid game tech? Maybe make roads > railroads > highways > automated highways > maglev trains? Each would give an additional movement bonus.
Diplomacy -- Give us a way to bully other civs without actually warring. Something like 'I see your troops on my border, move them or I nuke you" type thing. The diplomacy is lacking right now. I'd also like the ability to ignore a AI from useless spamming with open border requests. That could come back to "stop bugging me about it or we're going to war". Let me use my military might in diplomatic negotiations. With a revamp of spying like I talked about earlier, you could also give a demand to stop spying and if they don't the next spy caught would mean automatic war.
Give opposing cities that have your faith as a dominant faith a chance to flip and join your empire. Maybe use faith + culture. If you are the dominant faith and your cultural influence in that city is higher than the AI's, the city has a chance to flip and join you.
I've got many more ideas but they deal more with specific techs and stuff like that.