Hi Arkapravo,
As may be already aware of, a number of top universities, do provide a few courses on Culture journalism. PhD in this niche area may also be offered at these places. I am listing here a few universities which offer culture journalism and related courses and I suggest that you network with the professors or admission coordinators before you decide to apply for the program.
There are many others...These are not in any particular order. I suggest that you go through the university brochure and write to the admission coordinators regarding the program you aspire to pursue and get you in touch with the relevant person of the school.
Hope this helps,
Best wishes,
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