I don't "mind" hex tiles in principle (don't mind squares either) but the way Civ5 makes all land features conform tightly to the hex grid has got to go. I want land to look like LAND, not some jumble of Lego blocks. What that means is that there should be a jaggedness where a tile that's technically "sea" has some land jutting into it, and vise-versa. Civ4 did a reasonable job of this, so whatever 5 did to depart from it, dump it.
My other suggestions for 6 will use 4 rather than 5 as a baseline, that is, "do this to tweak 4" rather than even bother with salvaging 5:
1) 2 level game concept: Civ4's presentation of land and cities is pretty close to ideal as a *CAMPAIGN* map. The reason people wanted to push into some of the concepts Civ5 brought to the table was because it does not make for a good *TACTICAL* map. Rather than try to tacticalize a campaign map, the real solution is to make the game 2-level, the way the Total War franchise does. That is, you have abstracted icons for major unit stacks (which can even just be a "flag" on the map) in the campaign level, and in the tactical level, then it switches to the one-unit-per-tile concept, and each unit shows men in formation (e.g., a formation of spearmen, rows and columns, generally rectangular in shape). When attacking an enemy, the choice should be there to either micromanage the battle at the tactical level, or auto-resolve. When taking a city, there could be a choice to plunder the city at the tactical level to try to increase the amount of gold looted, or to command the men to treat the citizens well if you want to reduce the citizen resistance against your occupation, or some other tactics like maybe trying to discover relics or unique treasures--the game could make things a lot more interesting here than just "people scream".
2) Economy model: Civ4 is CLOSE to perfect "as is", but with these tweaks it could be much closer, IMO: one should never be able to "mine axemen out of the hills". That's a ridiculous concept. What you mine out of the hills is the metal with which to make the axes and armor, and on creating the unit you remove people out of the population and train them. You could have the most productive mine in mining history, but if your city has only 100 people you should never be able to blast out 6,000 axemen. This leads to a new concept to introduce, that of mobile commodity resources (quantities of iron, copper, etc.), and that weapons and armor should be one OF those mobile commodity resources. The production of a city requires a resource input, and its output can be a finished resource (weapons, trade goods, etc.) or a building or wonder. The latter is already represented perfectly by the existing Civ4 model, and the former would just be a minor tweak to it. Food would ALSO be a mobile commodity resource. There is no "verisimilitude" (the Civ4 approximation of "realism") in claiming that food cannot be transported from one city to another. It would have its COSTS of course (spoilage, bandits, etc.), but it should not be impossible. This would enrich the economic strategy of the game at the campaign level, creating new decisions to be made: should I keep all this food in a high-food city to generate Great People via specialists, OR... should I spread it out to other cities and allow them to grow more? That's a realistic choice real rulers would have made, that the game robs players of in the existing Civ4 model.
3) A few more "Sim King" perqs would be nice, as an option for play. A few random videos of maybe a king's banquet entertained by dancers or jugglers or fools--all tailored to the culture of the leader in question of course (maybe even stand-up comedians and rock bands for a modern ruler!) The player is pretending to be the leader of a nation, why not enhance that experience and make it seem more like that's what he or she is really doing? (Modders can probably take this into adult entertainment realms that need not be "out of the box" here, hehe...)
4) I have some ideas for resource tweaks, but those are very minor and can probably be modded in: tobacco, rubber, yew, and coca are things that either wars were fought over or were key resources that changed the histories of many nations. (Yew should also be required for building "longbows"!) Also temperate areas need more fruit resources to balance out what seems plentiful in the tropics but null and void at the higher lattitudes, so maybe drop in some apples or peaches or pears for food. Honey, hops for beer, etc. These are "nice to haves" though and not something to break the company's back trying to put in.
5) Ease of modding. I'm fairly computer literate but can quickly get lost in XML tags or unusual syntax in Python that doesn't translate to other programming languages I know. It would be HUGE, I think, if a Civ6 had a user-friendly modding module not too unlike Worldbuilder but which would also include unit customizations (like in Civ2 you could paste a graphic onto a reference sheet, add a line to an ini file, and voila, the unit exists), rule changes, and generally a richer ability to customize than what vanilla WB allows. Something more like Civ2's "cheat mode".
6) Real-earth maps and playable real-earth scenarios should be out of the box. It's ridiculous to force players to mod these on their own, c'mon people!
Other than that I'm pretty darned satisfied with Civ4 the way it is.