If you like sweets, I'd recommend trying ningyoyaki. You'll find ningyoyaki easily at Nakamise-dori, a street you will encounter when you visit Sensoji in Asakusa. It's a doll shaped pancake with red bean fillings.
I would like to recommend to eat Takenoko no sato.
It is one of famous snacks in Japan, it is made of chocolate and cookies. It cost about 200yen.
If you eat it, you will get sweet and lovely taste.
It is amazing.
There is also different version, it calls, Kinokonoyama. It's also great.
You can consider going to a local supermarket and pick up some fresh fruits, for example, peaches and grapes. They may cost more than you are used to pay for the same types of fruits in your own country but you will not be disappointed (I hope) with the quality.
If you like to try sushi, then you should go to "Tsukiji shijo"
It's a fish market where you can get a nice and fresh seafood or fish meal.