Missed most of this one, which is a shame.
Antananarivo [15] - Antananarivo is great because it has essentially no opportunity cost. You get more culture for just doing all the things you would do in an ordinary game anyway.
Auckland [15] - Not really committed to any particular victory condition, but just all round good. 1 Production early on for Coast tiles makes a real change as to how quickly you can get coastal cities up and running, and access the Lighthouse, plus it scales well later on too. Really nice City-State.
Bologna [18] (21-3) - Bologna is good but not so good as to be this far out ahead of the pack, particularly with how scaling for Great Persons now works. Surprised Antananarivo is so far behind relatively given these two both situate on Great Persons and Antananarivo arguably scales much better over the course of the game. I don't think Bologna is necessarily the worst but want to draw some attention to it and feel the lead is undeserved.
Caguana [9] - I'd have downvoted Caguana if I didn't want to draw attention to Bologna. The Batey is being very heavily overrated here, it's not
that good an improvement. In order to get the most culture of out the Batey you have to avoid harvesting Bonus Resources, which you shouldn't be doing at higher difficulty levels as the slingshot from harvesting is vital.
Cahokia [18] - Another really, really strong City-State. The gold from this can really snowball and like Auckland it's multipurpose and contributes to a wide range of win conditions.
Geneva [11] - I struggle to rate this one. It is good, but only because the AI is too dumb to nullify it properly. In MP it's literally worthless, in SP Deity it's actually a really good City-State.
Kumasi [6] (5+1) - I'm inclined to disagree with @bengalryan9 - I think that the yields from trade routes are much too significant for this to be better than Nan Madol. I agree that once you get Kumasi, you would rather run trade routes to City-States than other Civs/internally, but it's still a painful trade-off to make and can slow you down a fair bit early on. Nan Madol doesn't do this, even if Kumasi might be a bit better later on. Both very good though, and not a huge amount between them. However, I'm also upvoting because Kumasi is falling too far behind when there are worse options ahead of it.
Lahore [6] - Another one I'd have considered downvoting. The Nihang is not
that good, it is more often a win-more than something which turns a loss to a win or a win into a much faster win or more reliable win. However, I think Caguana is worse.
Nan Madol [10] - See Kumasi.
Rapa Nui [16] - in the right surrounding conditions, Moai are absolutely broken, in the wrong surrounding conditions, they're worthless. Hard to evaluate. I don't think Rapa Nui should be this far ahead of the pack, but I have other priorities.
Yerevan [19] - If this isn't the winner we just delete the forum, shut down the Civ series, and get on with our lives.
Zanzibar [16] - Zanzibar is another one sneaking by on not really being discussed, I actually think this is one of the weaker City-States remaining. I never find Amenities to be the road block in any of my games, Housing is the real limitation. Probably better than Caguana and Lahore but would definitely be looking to get rid of Zanzibar not long after.