City District, Settler and Building scaling cost. It sucks and I want it GONE. It takes much of the fun I normally would have out of the game for me (I always play wide on large maps. I love dotting the map with cities and seeing the AI do likewise), especially considering how weak IZs are at boosting production. It makes no sense that a city founded in 1900 AD has to spend 200+ years on building a harbor.
As for new features: Since we're getting Plagues, redesigned resources and enhanced diplomatic depth, I'll answer with enhanced happiness mechanics. The Amenity system is a bit bland and generic in how it works ingame and I would to see it reworked in a way that simulates how amenities work irl.
A hypothetic example: citizens that live in a city with a Campus become Educated over time. As their level of Education rises, they develop a need for cultural refinement, which can be satisfied by using an Amenity for Entertainment (provided by an Entertainment Complex) or by building an Amphitheatre in the city (which provide an Amenity SPECIFICALLY and ONLY for citizens with this particular need.). The first option wouldn't develop another need for the citizens. However, if a Theatre Square is built, your citizens become Refined; Refined citizens in turn develop needs for Education (build a Campus) and Prosperity (Build a Comm Hub). And so it goes on.
Entertainment Complexes/Water Parks, Holy Sites and Luxuries can be used satisfy unfulfilled needs of your citizens, depending on the type of need. Religions and/or pantheons too could be enhanced to do the same.
And finally, this would also allow for another mechanic I greatly desire in Civ. Every citizen in your empire has a distinct ethnicity based on the current population in that city AND loyalty pressure from nearby civs. Example: if an Assyrian city has a population of 5 Assyrians and 2 Hittites, there's a 2/7 chance the next citizen born is of Hittite ethnicity. This chance increases if the city loses loyalty.
Having too many Citizens of foreign ethnicity could for instance have negative effects your city depending on your relations with their mother country, reducing the city's loyalty, lowering amenities for the indigenous citizens, increasing foreign spy rolls. Unhappy foreign citizens are also more likely to become Domestic Tourists for their mother Civ, rather than yours. So you need to either work on integrating them into your society by increasing Loyalty generation in your city (creating a Law Enforcement District could help here; we don't have Police Stations and Courthouses yet) or "expell" the foreign citizens from your realm altogether (a friendly alternative to genocide). Integrating citizens of a different ethnicity in your cities generates diplomatic favour with their mother civ, giving you advantages in the World Congress, as well as a small discount (5%-10%) in cost for Techs and Civics their mother Civ has researched.
This same principle could also apply to religious citizens, who will demand you build Worship buildings specifically of their religion (would be nice if Shrines and Temples could also be assigned for specific religions if the need arose or if Holy Sites had areas of effect similar to an IZ or Water Park)
And FINALLY, I'll pick up on what Zaarin said about religion and name a specific religion thing: Great Prophets need to cost more points. Right now it's way too easy for an AI to get them because, you know, High Opportunity Cost + Low Actual Threshholds. For a human player there are only two ways to reliably get a Prophet: 1) Play as Arabia and 2) Play as Russia. By making Prophets more expensive however, you allow non-Arabia players to join the Prophet race, which indirectly buffs religious civs without Prophet generation bonuses such as Spain, India and Georgia.