8 a.m. is dinner time at the fish market! Still some activity, but nothing like there is earlier.
Ryokan often try to pack as many people to a room as possible--the charge is per person, not per room, so renting to one person doesn't make sense (for them!). That link from wres157 looks awesome. Take some earplugs, though, no matter where you stay.
Solidus has some solid recommendations. Great food in Chinatown. And Kamakura is cool, read up on the history of the area before you go and you'll get a great deal more from it (the era of interest is called the Kamakura Era). There is a ring trail that encircles Kamakura, pretty nice to get out and walk there, though you can't really see the sights from the trail.
Head to Shinjuku station and get out the south entrance, go to the Takashimaya Times Square building for a bit of shopping experience. Get there right at opening time (10 a.m.?) and walk through the department store. In the first five-ten minutes after opening, every employee stands outside their area and bows to all the customers. It's impressive to receive so many bows. It's also impressive to see how dressed up Japanese get on a normal day.
Takashimaya is a very expensive department store, but in the same building on the opposite end is Tokyu Hands, where prices are more reasonable (and has a section of souvenier type stuff that caters to foreigners).
Head to the basement floors of Takashimaya (or any other department store) around lunch time and get free samples of food, a cheap and entertaining source of nutrition. Games that you can play while you're there include spotting the most expensive melon and finding the most expensive cut of beef.
Isami is also in the same general area.
Head to Harajuku station for a sea of young Japanese trendsetters, and then around the corner to Meiji temple for a more traditional view of Japan.
Kyoto is well worth the trip if time allows, taking the bullet train is itself a neat experience but may blow any budget ideas you had. If you do go, sit on the right side of the train going, and left coming back, for awesome views of Mt. Fuji. And purchase your bento and beer on the train for the full shinkansen experience.
Enjoy!