You'll find the theatre inside the Times Square Shopping Center in Shinjuku. The zoo is inside Ueno Park. Take the JR Yamanote Line to JR Ueno Station. Tickets for the main observation gallery cost 820 yen for adults and 460 yen for children. The nearest station is Kamiyacho which is on the Hibiya Subway Line.
Entrance is free.
Leave Shinjuku Station via the West Exit. The ticket costs 130 yen and allows you onto the platform for up to 2 hours. The Science Museum in Kitano Maru Park has all kinds of interactive activities. At Tokyo Transportation Museum you can climb in and out of various engines and carriages and have a go at driving your own train through simulated Tokyo. Harajuku is on the JR Yamanote Line.