Go at the crack of dawn (like a bit before 5.30am) any day for the tuna auction, get a bowl of tuna sashimi at a stall, and then go take a nap at the hamarikyu botanical gardens nearby.
Such an incredible Buddhist Temple. It has like a million types of moss, and is a UNESCO World Heritage Site.
If you like cats, there are some cat cafes ("neko no mise") where you get a coffee or soda and get to play with cats for a while.
After you've seen the tuna auctions at Tsukiji, wander over here as it opens and get the garden all to yourself. Take a nap in the middle of it.
The gadget shops around Akihabara are pretty stunning. Be aware that most of them sell racks of porn as well.
This food theme park is hilarious and bizarre. It's in the Sunshine City building near Ikebukuru. 300 yen (~$3)
