In the city screen, on the left hand bottom corner there are two bars.
One bar says (for example) 100% Japanese - this is the city's culture mix.
The purple bar below it (with a musical note icon) says (for example) Refined (+13/turn).
Put your mouse cursor over the purple bar and it will say (for example) Culture: 525/5000.
This means the city radius will next expand at 5000 culture points, and you currently have 525 culture points.
Another way to see culture points is to look in the Domestic Advisor screen (press the house icon in the top right of the main map screen.
The culture points per turn (13) will appear under the purple musical note and the total (525) will appear under "TOT" column next to it.
