1. A balance pass for pantheons / beliefs. The best pantheons are, unsurprisingly, always the best ones. I get that because many of them are resource-based it's difficult to balance them since many of them are situationally powerful, but the strongest ones that don't have conditional terrain/resource requirements could be toned down a bit. Ideally the nonconditionals would be reliable if you don't have many of any one resource/terrain, but at the moment unless you have obscene amounts of luxuries or some other resource the respective pantheons are lackluster.
Personally, I don't think there should be pantheons that fail to provide anything after the classical era. Not unless they all peter out in some fashion. For instance, giving bonus GP points to campuses, theaters, and holy sites is certainly very useful for the entirety of the game (and the AI doesn't even like to take it). Maybe you should only get the bonus GP points until you actually have one of the respective GP's.
2. Harder Eurekas/Inspirations. As many have said, they're a bit too easy to obtain through normal play. They could be strengthened to compensate, but they should not be easy enough to obtain as a side-project while focusing something else; rather, they should be something along the way of whatever you're already focusing. Founding a coastal city for sailing is a good one; you might not aim for that Eureka unless you already want a coastal city or are planning one in the near future.
I think this sentiment (that has been expressed multiple times in this thread) kinda misses the mark with boosting techs and civics. Civ is not really a game where players all branch off into their own areas of research, and one guy goes researches economics while another pursues education while yet another guy goes after cavalry and siege technologies. Civ is, to a large extent, a game where the rule of thumb is that everyone generally does everything. You mention the Sailing boost for coastal cities. That's notable specifically because the marine technologies are the main exception to that rule. So, making boosts harder to come by is not going to make players more focused. Having research trees that branch off rather than all ultimately lead down the same path is what the game, and that's beyond the scope of small, quality-of-life improvements.
3. Related to above, slower science overall. Even the AI on prince is reaching the modern era hundreds of years early--alternatively, if the science rate is too drastic to change, just adjust the pace of the in-game years. I can accept faster science to speed up gameplay, but the year counter should at least match up roughly with tech eras at lower levels of play; it's simple, but helps a lot with flavor and immersion.
I think the way to look at this is that there's a pacing problem between research and production. You unlock three or four techs in the time it takes to build a district or just some walls. I get my encampment ready so I can bang out some swordsmen, and by the time I'm done I'm almost at musketmen. It's nuts, for sure.
4. Chopping nerf. I personally have never chopped woods for production in any game of Civ VI, but I don't want the feature to go away because it makes sense from a historical perspective. Gameplay-wise though, it's currently incredibly strong and only looks to be getting stronger in VI with the governor that boosts it. It could use some tweaking.
Again, to my mind it's a production problem. If forests and/or lumber mills generated an extra +1 production, the decision to chop them would be a lot more painful.
5. District adjustments. CHs and Harbors were at least looked at already, but Theater Squares could use some touching up as well; they do fine for holding Great Works but a bit more leniency with adjacency bonuses would make them more viable early game. More variability in district choice is nice for gameplay, and flavorwise once your discover Drama and Poetry and the like it does make sense that you'd at least have a few TSs. IZs could be boosted a hair too, but overall they're alright in the later game.
Yeah, theater districts should at least get +2 from adjacent wonders. Maybe +1 from entertainment complexes (or, conversely, have entertainment centers get an extra amenity from an adjacent cultural center. It can't just be odd to me that great works and tourism are not linked to entertainment amenities in any way.
6. Trade routes giving something to the receiving city. It doesn't have to be huge, but at the moment making your cities ideal for trade routes isn't very rewarding. You get roads to travel on and traders to pillage, but even then those same roads could be used to go into your city. There's also the fact that other civs are somewhat economically reliant on you if you're a main trade destination, but that's an indirect bonus that doesn't feel like much during actual gameplay. Even something superficial like a bit of gold at least presents something tangible to say "this city is the heart of trade".
Trade routes still feel like a tacked-on element in Civ VI, as they actually were in V. In fact, they seem even moreso, since they now lack reciprocity. To my mind, if there's no link between trade routes and the trading of resources between civ's, you have mismatched systems. It's a silk road without silk. Anyway, I expect the revamped alliances to build out trade routes, probably as one of the early bennies.[/quote]
8. The ability to ask an ally to declare war once you've been declared war on. Seriously, I'm not sure how this isn't already an option. This might be the military alliance in RnF, hopefully.
+1!