So, the game is starting to grow on me now.
As others have mentioned, culture grows your city at one tile per expansion instead of a giant circle at a time. This relieves the pressure from having to buy land. Now I see buying land more as an option and a tool instead of a necessity. You have the option to buy that resource you need instead of waiting for cultural expansion to get to it. Or you can buy that row of land between you and another civ to ensure it is in your empire instead of his. And the expansion through culture seems to be intelligent, as by my experience so far, it expands towards the most beneficial tiles first.
The build speed of cities seems to catch up once you hit the AD's and start to have more than just 2 or 3 cities. You still need to be sure to be picky about what you build, but it isn't as bad as the early turns when you have 7 buildings you want, 3 different military units and next turn you'll have 2 more to choose from! It is just mass overload in the beginning.
I really like puppet-states. Usually in war you don't want to add a bunch of new cities either because you didn't want the extra cost associated or you just didn't want to manage the city while controlling that large military. Nice thing about puppet-states is that you can take full control of the city at any point. Even better is that you do not have to make the decision if you want to keep a city as soon as you conquer it. You can go ahead and keep it, and then look at what improvements, resources, etc it has, and if you don't like it you can still choose to raze the city! And razing isn't instantaneous now, it actually takes time to burn that city to the ground, which gives opponents time to reclaim a city if you decide to raze it.
I have found city-states can be quite grateful when you save their ass from another civ. One of the city-states I was allied with was attacked by another civ, and this city-state gave me a quest to destroy at least 3 units of the attacking civ. I was going to anyway since the city-state was giving me iron that I could not lose. After completing the quest, my reputation jumped by around 150 points. Completing quests to remove barbarians gave around 50 points. I imagine liberating a city-state that has been conquered already gives a lot more points. You still have to spend gold most of the time to keep city-states allied, but it is nice to know some quests have appropriate rewards.
Once again as others have mentioned, 1 unit per tile and hex grid really, really is the shining star of this game. Combat is so much more interesting now. I think it is the one thing that makes me say I would rather play civ5 than civ4.