Hi, I usually play on Emperor/Immortal, standard speed, with no mods except 4 uc and Enlightenment era.
One of my main issues with naval combat is naval promotions. The upper level promotions, especially for naval melee units, are really fun and interesting as they typically allow the unit to do things it otherwise wouldn't be able to do (gain gold from combat, heal outside friendly territory etc...). However, because these great promotions are hidden behind 2 or 3 less interesting promotions, it makes early naval combat less dynamic and mid-to-late game naval combat dramatically stronger. My suggestion would be to put just a few of the cool tier 2 and 3 promotions behind the tier 1 promotions to allow for early naval units to be more interesting.
Another issue I have is with the pace of the game, namely that the classical and medieval eras seem to go by extremely quickly. If techs in these eras could cost 10-15% more I think that would make the game much more interesting. The action that goes on in these eras really seems to determine whether you'll be in the running to get a VC in the late game, so it seems odd that this stage of the game is so quick.
This may be a slightly controversial take, but I think fewer players should be able to found religions, and religion should affect diplomacy more. Currently 4 out of 6 civs on a standard map can found religions. One of these religions may die out, but in most of my games it typically turns out that the two strongest civs each have one of the two weakest civs following their religion, and then the two middle civs are the only ones following their own. This means that using religion to form alliances with genuinely powerful civs is almost never an option. I would suggest just having 3 religions for a 6 civ game, and increasing diplomatic bonuses/penalties for following a religion. I would also increase the importance of religious pressure. Currently religious pressure seems pretty meaningless, even though it requires investment and strategy just like using missionaries. Part of the drawback of selecting a building as your first belief is that it delays building of missionaries, so the religious pressure you get from them should at least partially compensate, but currently it barely does anything. Of course, if religious pressure were buffed, I would slightly nerf some of the strongest religious buildings.
Currently, going to war always rarely seems worth it unless you have some combination of city-state quests, weak neighbors, or nearby cities that will be hard for the AI to defend. I feel like this disproportionately hurts peaceful civs and benefits warmongers. I would increase the benefits of fighting wars not focused on conquest by increasing the yields garnered from pillaging tiles. I would do this by giving 3-5 turns worth of the tile's yield to the pillager's nearest city, in addition to the small amount of gold and HP boost. Especially in the early game, pillaging tiles gives very low yields. To balance this out with warmongers, I would reduce the gold earned from conquering a city.
I'll also mention the balance between siege units and ranged units. They are just too similar in capability and should be further differentiated. Siege units should be even stronger against cities but even weaker against units. Honestly, even though it was annoying to deal with in the base game, requiring siege units to set up does make a lot of sense. With how they are balanced right now, especially with how weak archers and compbows can be at certain stages of the game, it almost always feels better to just build siege units even if I don't think I'll trying to take cities. If I need a medic, I'll just build a skirmisher. I really liked Pdan's suggestion for splitting the archer and compbow into three units, as I think that will partly solve this problem, at least when it comes to compbows and catapults.
