One of the interesting building that you see in the west Skyscraper district of Shinjuku (Nishishinjuku) is the Sompo Building. It looks like this:
You'll notice the possibly even more interesting Mode Gakuen cocoon building on the right.
One reason you might like to go up the Sompo building is that there is an art museum on the 42nd floor. While I was there I saw the Jeux Surrealism exhibition. It is also possible to see one of Van Gogh's "Sunflowers" paintings here. Another good reason is the view.
Pretty damn fine.
You may recognise the intersection on the left as the same as the background of my blog. If you look closely you can see Tokyo Tower, and even more closely the Tokyo Skytree.