Maybe mountains and hiking? Tokyo is considered to be a city, but there are a lot of nature in the west part. Mt.Takao and Okutama hiking trail are must visit places if you enjoy being in nature :)
I am not sure if my answer is Secret. .
There are many kinds of food in Tokyo.
There are many Tokyo-like Japanese food, but also food from all parts of Japan gather in Tokyo.
Since you are coming to Japan, why not try many kinds of food?
For example, sushi, soba, noodles, eels, bowls.
I think that these can be considered as Japanese foods that existed since the Edo era.
How about feeling the Edo period through food?
Also, the color varies from town in the same Tokyo.
I think that it is good to study various cities and take a walk.
For example, Jimbocho has many bookstores and coffee shops that have been working since long ago.
Relatively, I think that there are many shops and buildings that have done since long ago in the eastern side of the Imperial Palace a bit.