I'd like to see someone try to explain my situation here:
I'm running a core i5 6500 @3.2 Ghz, a Nvidia GTX 1070, and 16 GB of RAM. At max settings, while the camera is positioned over revealed terrain with a lot of detail onscreen, so that would be over my cities with lots of tile improvements, when the camera is zoomed out all the way the FPS drops down into the 40s and there is a very noticeable amount of stutter that occurs. If I zoom in a certain amount the stutter goes away and the FPS improves somewhat, usually going up into the mid 50s. Normally I play with Vsync turned on since there is a lot of screen tearing that occurs if I leave it off.
Now this is very situational; it only happens when my camera is positioned over revealed terrain and there are a lot of tile improvements. Just for testing purposes I lowered all the graphics settings and turned Vsync off and my FPS shot up to about 100 or so, while the stutter went away.
My computer shouldn't have any trouble running this game; this is a computer that can run Witcher 3 with Hairworks at max settings 60 FPS at 1080p, and neither my video card or my CPU are working at 100%.
So for anyone who says that their game runs fine with no hitches, try loading a save game, positioning the camera over revealed terrain with a lot of onscreen action (tile improvements seem to be what is bogging my system down), and let me know if the game stutters, if your FPS drops, whatever. If yes, then there's an issue with the game engine. If no, then I guess I'm just cursed.
Oh and make sure your camera is zoomed all the way out also.
Most likely graphical driver. Try monitor your GPU usage and tell me the result.
I'm not exactly sure how much knowledage you have towards hardwares and game optimization in general.
So I'll try to explain as many things as possible concisely.
1070 is a pretty new card. So the first few drivers fail to bring out all its power is not unheard of.
In fact, rather common in recent years since NVIDIA adopted a "one best driver for a few games".
Check if you had the optimal driver for Civ6 installed, which is 375.63.
And then, Civ series is always rather hard on the CPU, and i5 6500 suffers a little because it doesn't have HyperThreading.
Usually it won't affect things too much, but it's clear that you just upgraded to 1070, which require a powerful CPU too.
The 6500 could be struggling at dealing with game's processing and gives out rendering command to the GPU.
Lastly, check your cooling and PSU. Make sure you have enough power supply for it and the GPU isn't too hot that it throttled.
Though I really doubt that is the case here.
EDIT: What's your native resolution? It could simply because you're running 4K with 8x MSAA. And nothing would handle that well atm.
Actually, I wouldn't even recommend 1080P with 8x MSAA. 4x is enough for AA alone. You are better off with supersampling if you had the horsepower to spare.