#1 is the main priority; all other points are subordinate to it, in no specific order.
#1 Make an AI that can actually play the game on a *semi*competent level. Whenever you implement a new feature, ask yourself this question: 'Can the AI be made to handle it reasonably well?'. If the answer is 'no' or 'maybe', then scrap that feature or alter it.
#2 Make it possible to have HUGE civilizations, with 100+ cities in them. I want to manage an EMPIRE, not a petty principality. However, a principality should still be a viable option. Perhaps make it so that you can build multiple copies of regular buildings, but they get more and more expensive as you build more in the same city? This way a 'tall' empire would have 10 Factories in its single city, while a 'wide' one would have 10 cities, each with 1 Factory in it. Tricky to balance, I'm sure, but that's what you're being paid for.
Also, having 100 cities should take every possible supporting building/policy/etc just to make it viable.
#3 Streamline the interface (no renewing deals every 30 turns...), so you get the info you need when you need it, no less no more. Make everything about it moddable ofc.
#4 Ensure that making mods is far less clunky and unintuitive than in Civ V. At the very least make it so that *maps* do not have to be made into mods to be uploadable into Steam.
#5 Tone down the graphics to accommodate the huge civs and better AI. (I know, won't get my hopes up, but still.) Personally I'd prefer it if the game looked like Civ II but everything else was modernized; imo that game achieved the perfect balance between aesthetics and informativeness.
#6 Get the tech tree right for once. There should be real trade-offs and decisions. Hack Science to little pieces to end its dominance for all I care; I do *not* want *every* game to be about Education beelines.
#7 Make food (and maybe production) global from a certain point in history (or in increments with more and more advanced techs). I want my breakbasket cities in the Ukraine to support my mining colonies in Siberia. Civ V did this to an extent, but the food wasn't subtracted from the 'donating' city. Corporations could tie into this mechanic; there's much in the way of fresh, unexplored territory here.
#8 For God's sake get rid of the late-game slow-down/bogging down problem. It's tough enough to micromanage 1,000+ troops without my computer freezing due to memory leaks and fancy graphics... Also, related to this, the AI should be a challenge right up until the end. Some have toyed with the idea of increasing, game-long bonuses for the AI instead of (/in addition to) the one-time starting boost that it currently gets. I'm all for this idea, provided that it doesn't apply on the lower difficulties. We were all noobs once, and sometimes one simply wants a nice stompy-face game, with minor distractions from the victimized AIs.
#10 Working multi-player. 'Nuff said.
Etc etc... I'm sure I'm forgetting loads of things. Really though the AI is crucial for a true enjoyment of a Civ game imo. If it means 1upt must go, then so be it. The world *can* resist an idea whose time has not yet come, after all.