If you like history and culture, Ueno would be a great place to spend the day. It's the first major stop in Tokyo when you're coming in from Narita so the journey would be around 60 minutes one way.
There are the art museums here which are fab - some very special Asian art is stored here. There's also Ameyoko shopping street - lots of street stalls selling all kinds of goods. This used to be the black market area during WWII and although it's nothing like as cheap as it used to be, it's lots of fun to wander round.
There's also a big park here (Ueno park believe it or not)! Lots of trees, some buddha style architecture and older buildings - so maybe this is a good choice for you
