Perhaps Shinonomemizube Park, the bridge to Tatsumi subway station, and the green areas around there. You'll be close to the Tokyo Bay area. The rather unique architecture and layout of the UR Shinonome housing complex and its surrounding area was quite nice. Unfortunately the park would not really win the grand prize for its breathtaking aesthetics. The area was mainly designed to be functional.
If you prefer the scenic route, you'll probably appreciate Hamarikyu Gardens near Shimbashi, which puts you near the Sumida River. Perhaps also Kiyosumi Park and its associated garden. However, I would not really consider them unknown.
If it is okay to go a bit outside of Tokyo, check out the area around Yokohama Port. The Yokosuka Line can take you there and back. It may already be too far for you though. If you do go, consider the area around Red Brick Warehouse, Marine & Walk, etc. Nice views, a lot of things to do, but unfortunately not exactly unknown either. :<
But I hope it helps.