Most people probably think that the centre of Tokyo would revolve around Tokyo Station, but unlike other cities, Tokyo doesn't really have a centre (closest would be Shinjuku, or if you're looking for younger lifeforms, maybe Shibuya).
Tokyo Station is usually devoid of much life save for the odd, (ha, like most of them aren't) salaryman.
I found it quite by accident. Underground, there is an interesting corrodor of shops called Tokyo Character Street. So, you want to get a little Hello Kitty, Rilakkuma, Totoro souvenir?
It's been open since July 2011, but I didn't know about it. I was after a wind-up Domokun toy for ages ever since the big Kiddyland closed down for renovation. So luckily I found one at the NHK shop here.
Don't know Domokun? :O Here's an appropriate video ;)