This building, the ‘Tocho’, was designed by Japanese architect Kenzo Tange. Apparently, it was inspired by the Notre Dame in Paris. I liked this paragraph describing the area;
Compared with the sparer lines of most of the skyscrapers that surround it, the traditional grandeur of the cathedral is certainly apparent in its complexity of structure and surface, not to mention its equally grandiose sprawl. The complex also incorporates the 37-storey Tokyo Metropolitan Main Building No.2, and the eight-story Tokyo Metropolitan Assembly Building. Taking up as much land as it does, the whole Tocho complex is like a town unto itself, and, walking around and through it, with its heights, depths and multiple levels, unless you take great care to ascertain your bearings, you are likely to get lost.
Utilising the free access to the viewing platform is recommended. The view is quite spectacular, in a anthropogenically perverse way. At ground level, it's easy to forget you're stood in the world's largest metropolis. Going up the tower should remind you!
There's lots to see and do in this area of Tokyo, though most of it's underground (in the B1F areas of these huge buildings). Restaurants, coffee shops, retail shops, barbers... you name it! It's easy to miss the underground complexes with such monstrous distractions looming overhead.