Joe asks me: "Do you often go to the cinema?"
I reply: "No, I have not been to the cinema for a long time"
This is correct.
But can I say:
"I have not gone to the cinema for a long time"
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I have not gone to the cinema in a long time
I have not been to the cinema in a long time
I have not seen a movie in a theatre for a long time
All have basically the same meaning that you have not seen a movie, eating popcorn and drinking soda, in a building for a while.
The present perfect is used since it was a situation which began in the past and continues
(Please note: This answer has an American English bias.)
A natural response would be
No, I haven't been in a long time.
You could also use gone.
Notice: in a long time. This seems more likely here, although there's nothing wrong with for a long time.
I wouldn't repeat cinema in my response. But if I wanted to include the destination in my response, I would rarely say cinema (which is more characteristic of British English).
In the US, movie theater is probably more used more often than cinema. But in American English we would most likely say
No. I haven't gone to the movies in a long time.
The movies is the usual expression used in the US to mean cinema. See Why do you say "to the movies"