Next look for the Tokyo Metropolitan Government Building. With Notre Dame in Paris apparently and clearly the inspiration, you won't mistake it. The building, the fourth tallest in Japan, was finished in 1990. It's 296 meters high and thanks to special shock absorbing pillars and posts, it's supposed to be fully earthquake proof. There are two observation galleries, one in each tower at 45 floors up.
Entrance is free and the panoramic view is fantastic.
It's not particularly picturesque, but you may find it socially interesting - much of it is a shanty town inhabited by down and outs. On some Sundays a flea market is held in the entrance - see the listing magazine Tokyo Classified for details. Just over the road from the park you should be able to see the Century Hyatt Hotel. With this and the Tokyo Metropolitan Building facing you, turn left and walk towards the set of traffic lights. At the traffic lights turn right, and then make your way back east to find Shinjuku Station.