Alright then.
1. City-states built out more. They're a cool concept but the implementation isn't deep enough to go anywhere near tapping their potential. In particular, I'd like to see quests and diplomacy become primary in becoming friends with them, and I'd like to see a continuing relationship matter (instead of just buying them up the turn before a UN vote). I'd also like them to be a lot more dynamic militarily; I want to fight wars by proxy when it's appropriate, and I want to end up in a situation where I have to choose whether or not to honor my commitments to some minor civ when it risks war with a great power. There's no real way to do this right now, and it's rarely if ever a real choice.
EDIT for clarity: I'm NOT talking about more variety here. I'm playing a game with the Not Another City-States Mod active and frankly it very quickly dissolves into cacaphony; city-state type has lost all meaning to me in this game. I'm talking about more gameplay around your relationship to the city-states around you, regardless of what type they are.
2. Specific eras in the game built out more. In particular, I want:
a) A deeper Classical era. Right now the Classical era is just something you jump through in a race to the Medieval. I want depth in this part of the game.
b) A deeper Age of Sail/Renaissance. I hate the Musketmen -> Riflemen jump; Musketmen seem to be 16th century gunpowder, and Riflemen seem to be 19th century infantry. There's a huge gap between these two eras; the American Revolution and the Napoleonic Wars were fought entirely by gunpowder-equipped troops and with lots of field artillery/cannons, but they were fought entirely differently from the American Civil War (I'm a yank and I refuse to be politically correct, so if you want that written out as war between the states, too bad), with technology which was far inferior. Basically, I want the Age of Discovery/Age of Sail/Napoleonic Wars to be differentiated from both the Renaissance and the Industrial Revolution.
3. Colonies. I want to want to impose my will on all those random city-states and weak empires on the other continent, random island chains, etc., and I want to go settle all that beautiful unclaimed land, regardless of what kind of victory condition I am aiming for. This is one of the biggest things that distinguish the 17th, 18th, and 19th centuries from the previous millennia, and I want it in Civ.
4. International Trade. In the real world, Constantinople was one of the absolute most important cities in the entire world until only a few hundred years ago because of its location; all trade from the East flowed through it. I want this kind of geopolitical concern to matter. It should of course be simplified down into easily managed game concepts, but it should exist in the game.
5. Victory rework - this one's almost certainly off the table for actual game development, but the concept that Civilization should end with a single, discrete event is patently silly. Give me a set of goals in each era (and rotate them era by era!), give me a huge points bonus for accomplishing them, and then give me points era by era, with each era being weighted equally. Dominate the early game and then fall off to obscurity? You're Rome or Greece. This is, by the way, a huge reason why there's tension between the AI playing to win vs playing realistically. With a game with discrete win conditions, if you're 50 turns from a probable UN vote, doing ANYTHING that gives your strongest rival more gold is a bad idea, even if it's what's best for your empire, because the game is going to just end in 50 turns if you don't stop them. A different approach to what it means to win a game of Civ would eliminate that tension, because in almost all cases doing what is best for your empire could be made synonymous with trying to win the game. It's really not impossible to do.
By the way, I'm firmly convinced there will be an expansion pack. I don't have evidence for it, but I do think it will happen.