There are lots of anime fans all over the world, and Japan does promote the industry to boost tourism.
However, I am unaware of any animation studios that allow visitors. I'm sure a lot of visitors would like to peek inside and see what it is like - perhaps not the working areas, but the general surrounds & going-ons.
I have noticed one tour group doing such a trip - but for the traveller who goes without a guide group - are there any options?