The Tokyo Metropolitan Government Building has two observatories that are open to the public and are free to visit. The observatory is located on the 45th floor, and is close to the Shinjuku station, and right next to the Hyatt Regency Tokyo.
The South Observation deck is open daily from 9:30 AM – 5:00 PM (and until 10:30 PM the 2nd and 4th Monday of each month), while the North Observation deck is open daily from 9:30 AM – 10:30 PM.
The observatories are closed with the following schedule: 1st and 3rd Tuesday of each month (South Observation Deck), 2nd and 4th Monday of each month (North Observation Deck). If there is a national holiday on one of those days, the observation desk will open on that day, but will be closed the following day.
I went after 5:30 PM, so was directed to the North Observation deck. There can be wait times, especially if wanted to go at sunset, however I only had to wait about 5 minutes during my visit.
There are some neat views of the city, but going to see the sunset would probably be pretty spectacular.