Immortal, shuffle map, random leader, try to role play the leader. You'll have your fun at least 100-150 turns. I don't want to be rude, but it's almost insulting to say you play on prince and find it boring - that's because you are playing on too low difficulty for your skill.
That almost sounds like a wife making excuses for her abusive husband..
Unless you're playing *way* below your own capabilities, the game should be fun on any difficulty-level - and it should be fun all the way through. I shouldn't have to "cheat myself" and "role-play" the game in order to make it fun.
I've been playing on three different levels now (prince, king, emperor) and the pattern is always the same (more or less).
1. AI will give you early/very early aggro but isn't really capable of threatening you. They can mess up your game by pillaging and/or by making you switch to full military production when you still only have 3 or 4 cities, but I've never, ever lost a city to the AI yet.
2. Once you kill enough of their troops, the AI will peace out - usually giving you excellent deals for no real reason (gold, GPT, even luxuries).
3. Since now you're in the full military-mindset and probably have a sizeable army too, you can easily declare on one of your neighbors, taking a city or two for yourself.
4. In some cases you'll get declared upon by other AI who often don't even bother to send troops towards you. They too will usually peace out and grant you good peace-deals (for no reason).
5. By now, you're at least in the classical era where the AI gets less and less likely to declare out of nowhere (plus you now have a pretty strong/experienced military to deter them anyway), so now it becomes a race to see who can grab the most land.
6. Unless you want to go for domination: Decide on victory condition, build up your infrastructure, while also grabbing all the land you can get and let the game run until you win.
The only differences between difficulties that I can see is that the early aggro is a bit more challenging the higher the difficulty-level gets. That and the fact that the AI-boosts get pretty insane the higher you go and that they don't *need* to build up their cities in order to be competitive.
Sadly, building up your cities and your government in a smart and foresighted way doesn't seem to get you the kind of rewards you got in Civ V. In the old game, you could easily out-tech AI civs that were focusing on other aspects (religion/military/culture). And once you adopted Rationalism, you could *really* leave the AI in the dust. Not so in Civ VI where the AI seems to compensate for its lack of science-buildings/policies with sheer population and "cheating"-boosts.
Personally, I really enjoyed going tall from time to time in Civ V - India and Venice are two of my favorite civs in that game. Sadly, Venice wouldn't even work in Civ VI with its current mechanics.
Example from my recent King-game as Germany: I had 13 or 14 cities (including three ex-capitals), most of which had fully upgraded campuses. I also had all the relevant instant and permanent science boosts through Great People (Isaac Newton, Charles Darwin, etc). I had the GL and Oxford University. My closest rival (Scythia) had even more cities, but no campuses in any of them for much of the game (checking her cities in the spy-management-screen revealed that). She also didn't get any Great Scientists ... but she was actually ahead of me in tech for the longest time.
S.