Shinjuku Gyoen is famous for its chrysanthemums in November. The publicly accessible part of the Imperial Palace grounds (in addition to Kitanomaru Park) has a section that features every tree that grows naturally in Japan and is a pleasant walk in any case. There is a small museum on the grounds that displays a rotating selection of traditional art from the imperial collection.

I recommend the boat ride between Asakusa and Hama Rikyu. It's not by any means scenic or historic, although you do see the remnants of the old canal system that are now used for flood control, but it's a pleasant and relaxing change from the frenetic activity of the subway or Yamanote Line.