One thing I've definitely noticed is that the AI almost never suffers from unhappiness.
In my current game, I've used great generals (with Lebensbraum) to steal a bunch of Siam's territory, completely cutting off some of their cities. I then went and sanctioned them in the WC for good measure. I installed spies in them to see if they were hurting, and nope—even with a only a few tiles in a 24 population city, they're chugging along completely fine.
So, a few suggestions:
1. I would say that happiness needs to be an issue for the AI, but thinking about it, why is happiness even an "issue"? Having high happiness, middling happiness, low happiness—all of it is just a gameplay mechanic that should have play styles available to deal with. For instance, middling happiness empire but decent military strength: garrisoned units could act like inquisitors do "purge" the unhappiness. With low happiness but high military strength: a city rebels but you quash the rebellion, that city should be "made happy" for a decent number of turns afterwards. Further, putting down a rebellion should give additional benefits that help that play style. On the flip side, if you're playing diplomacy or culture and don't have the military strength, there should be different tools available. Public Works is in the right direction, but that's something that could be expanded on: different types of Public Works that give certain benefits when completed, or that are based on cultural/scientific output. Alternatively, if you have high income, "buying" happiness could be another option (and there is some real world precedent for this—oil-rich countries have been doing this for a while).
2. Tourism needs not really an overall or rework, but an expansion of its mechanics. It's weird because it feels like a raw resource (similar to gold, faith, culture, science, etc.), but the player never really gets to distribute it or "spend" it. I still advocate for a way to peacefully conquer or flip cities (I know this is technically possible but I've never seen it in game), and tourism seems like a good candidate to implement this. This doesn't have to be the only use for it, but it's just an example of how a military/expansionist focused civ can use this resource as a new tool instead of units/settlers. Diplomacy focused civs could use tourism to negotiate better deals with the AI or have their WC proposals be more liked by other civs.
3. Warfare is weird in Civ 5, you start with a very low military supply cap and early battles are usually the most fun. At some point though, the sheer amount of units makes war a boring task of chipping away at enough enemy units while not particularly caring about positioning or tactical placement. While a lowered supply cap is part of this solution, having artillery units (or range units as well) deal splash damage by default would help. I'd also consider having later game ranged units be capable of an overwatch mechanic, similar to air units ability to intercept. In any event, units seem to die too quickly to earn enough promotions to be valuable, or have too many promotions and be unstoppable. Some type of forced retreat ability, or an ability that Naval warfare and city sieges always felt strange, because you can usually capture cities but are defenseless at holding them. An unintended effect of this is that it's a great way to raze cities—every time you capture a city, you can move your melee naval unit out, have the city be recaptured (lowering its population), then recapture it again (further lowering the population), etc. until you can raze it in a turn or two. Either naval units and land units need to be merged somehow or allow them to switch between different unit types.