Free View: Gazing at Tokyo from the Bunkyo Civic Center
Although it's one of the shorter decks in Tokyo, the Bunkyo Civic Center observation deck has some great views.
If you start on the east side, you are first greeted by a nice view of Tokyo SkyTree. While it, too, is an observation tower, SkyTree is now a very important part of the Tokyo "skyline" and is pretty heavily photographed. Since it is out in Asakusa, it stands almost like it's all alone, towering above the rest of Tokyo.
You can look down at the city. This is a great place to get a better feel of how Tokyo looks as a city full of houses and people, not just the face of major shopping districts in major tourist areas.
In the middle is a window into the civic center. I have no idea what exactly happens in this green room - probably some city council meetings or something.
Continuing around, this is the view towards the northwest. That should be Ikebukuro off in the distance. Tokyo is quite flat.
One of the benefits of getting a bird's eye view of an area is that you can discover new things - like this green space right next to the civic center.
Unfortunately, the south side of the building has a restaurant so you can't really look over the stadium and amusement park. It might be worth grabbing lunch if you want to see that direction. But if your visit is timed right, that's not the best view.
This is the skyline of Shinjuku. My visit was on a fairly hazy day, but it is possible to see Mount Fuji just behind the skyscrapers on very clear days:
The observation deck at Bunkyo Civic Center is open from 9 AM to 8:30 PM, almost daily, and admission is free! The center is pretty convenient, served by multiple JR and subway lines - the closest stations being Kasuga on the Mita and Oedo lines and Korakuen on the Maranouchi and Nanboku lines. It's right across the street from Tokyo Dome, and thus is a perfect addition to a trip to the amusement park, garden, and/or stadium.