Get to Tsukiji fish market early, using either Tsukijishijo or Tsukiji station, when you?ve had your fill of gawking at fish walk to Hama Rikyu gardens and take a stroll. After that you have a few options.
Shiodome, Ginza and the Emperor?s Palace
This doesn?t involve any train travel and is all in the same area. From Hama Rikyu walk to Shiodome (pronounced she-oh-doh-may) and take the glass elevator as high as it goes for a look over Tokyo bay, Tsukiji, Hama Rikyu and Odaiba (check the map closely - there are 3 buildings in the complex). Shiodome also houses a TV station, a theatre and an ?advertising museum?.
From Shiodome its a fair walk through Ginza and Yurakucho to the Imperial Palace so take your time. The palace itself isn?t open to the public except for special days and for pre-booked tours, so the most you?ll see is some bridges, gates and moat walls. If you?re still up for more walking by the time you?ve finished at the palace you can keep going and see Yasukuni Shrine which is at the top of the gardens, opposite Budokan.
If you?re really slow and are finishing up about dinner time, you can head back the way you came and try one of the funky bars and/or izakaya wedged under the train line. There?s also yakitori alley, which is a bunch of semi-covered stalls selling BBQ chicken and draft beer... although I can?t really recommend it for the food, the atmosphere is interesting.
Plus Shiodome and Odaiba
See above for the Shiodome part and from there take the Yurikamome Line from Shiodome or Shinbashi station to Daiba station on Odaiba for Decks and Aqua City and the beach, or keep going to Aomi for Palette Town and Toyota's Mega Web. You can get off at one and walk to the other, it isn't too far.
Plus Asakusa
From Hama Rikyu you can take the ferry to Asakusa. I?ve never taken it myself and I?ve heard mixed reports about it but if you think of it as just a ferry instead of a river cruise you shouldn?t be disappointed. The ?river? sits quite low so you don?t really get a good view and, to be honest, there isn?t that much to see anyway.
At Asakusa you can visit Sensoji and then take a walk through the back streets. If you?re up for it, Ueno isn?t far from here and neither is Akihabara.