If you can drag yourself out of bed early enough, venture out to the Tsukiji Central Wholesale Fish Market for a unique local experience in the middle of Tokyo.
The fish auction starts at 5AM for seafood wholesalers, and restaurant owners get in on the action of the auction at 7AM. There are about 1200 wholesaler shops, along with some sushi bars and food stalls. It is fascinating to walk about and see all the variety of the "catches of the day". Take a casual stroll around the many stalls, with all sorts of tuna, squid, crab, shrimp, and other you-name-it-we-got-it sea creatures. Some are still kept alive in fish tanks or big styrofoam buckets, and the locals take great pride in handling the fresh seafood. Most of the seafood products are sold to large and small local restaurants, but some small portions are also sold to individuals too.
The locals here do not seem to mind that tourists come out to check out this free-form equivalent of an aquarium, as the early hours holds the potential size of such a crowd down. Just stay out of the way of the men dragging huge slabs of fish and fresh seafood, some riding in little motorized vehicles. Do not wear your finest outfit here, as water and flopping fish and whatnot may splash you! The surrounding neighborhood is relatively blue-collar and faceless, but you are not far at all from the action in central Tokyo.