I think there are many way to write it, there aren't any reason to define what is "natural" and what isn't. The first sentences is wrong (It is difference between each sentences).
There is no place in India where rice is not eaten.
There is no place all over India where rice is not eaten.
There is no place in India where people do not eat rice.
These are right.
There're other way to write that, You can use There isn't any place in india where people don't eat rice. or Everyone in India eats rice too.
I think the best ways are Everyone in India eats rice and There isn't any place in India where people don't eat rice.
Why? Because I noticed that in English short sentences are often used and a lot of English people prefer use any than no.