Now that the Narita bunkie trip is a 4 day, that might give y'all some time and incentive to get out and about the neighborhood of the hotel. In a short 35 minute walk's time, you'll find yourself in the grand park and fortress are of the Imperial Palace. I had read online that the East Gardens are free. Even though that did not include a newspaper, I decided to give it a shot. A tour of the Imperial Palace requires an internet reservation, so I figured I'd try to snag that one on my next Tokyo layover.
It's really easy to get there. Out of the ANA Intercontinental, hang a right. Turn right on Route 405 (Sotobori Dori) and after a few block, turn left on Route 301 (Uchibori Dori). This will take you past another cool little park called Hibaya Park, which is worth a walk through if you have the time. Optionally, you could just stay on the street the Hotel is on until you get to a moat.
If you are a jogger, you won't be alone jogging around the palace outer grounds. It's a very popular jogging location for the natives. (see this article)
Along the way (or return) stop by the Nijubashi Bridge, with the picturesque view of the Palace in the background.
The East Gardens park is free, but it has some odd hours. From Nov - Feb, it closes at 4pm (5pm Apr - Aug, 4:30pm all other months). The bicycle-riding guards will not let you stay a second longer. It's also closed on Mondays and Fridays. (see this Japan Guide article)
On the day of my trip, the sky was overcast, so the colorful fall foliage lost some of it photogenic lustre, but it was still a pretty sight.
I plan on taking the Imperial Palace tour next time. If someone has done that already, post a response here with your insights.
The public square outside of the Nijubashi Bridge is huge and is home to many well manicured trees.