Figured I'd circle back since you're probably in Tokyo already. Did you rent a wifi passport? It'll help out greatly unless you have a sim card there, or tmobile since you get free international data. There's a bunch of places to go, but here's just a few of the many places that I went to in April last year. 8 days wasn't enough for me to explore Tokyo.. I probably needed another three weeks to take everything in.
History Garage/MEGAWEB
On your way to MegaWeb from Diver City, you'll spot the mini Statue of Liberty
If you like extremely spicy food, I have a spot for you!
Unfortunately I forgot what park this temple was at.
Shinjuku Gyo En National Park. Loved it here. Fantastic place to walk around and have a picnic if you'd like. Costs a few bucks but well worth it.
Meiji Jingu torii
Wander around the Yodobashi Camera shops. There's awesome shopping and cool things to look at everywhere.
Tokyo Metropolitan Government building- You can see Mt Fuji from here if the skies are completely clear
Walking around Coredo Muromachi
Feel free to pm me if you're looking for something in particular!