Yes, I agree with Sangetsu. It is definitely feasible... though it would probably be better if you got a morning flight and didn't leave until late at night
I also agree with Sangetsu on the Yamanote line... it takes you everywhere. You can get off at each stop and take pictures without having to pay the ticket (unless you leave the station platform). Just make sure you remember what color green the yamanote line is (they colorcode the lines) because I remember there were two greens, a lime green and a regular green.
You also might see people swiping their suica cards instead of actually putting in a ticket... make sure you don't be the idiot I was and actually try to swipe the ticket instead of putting it in the feed!
I did Shibuya, Akihabara, and Shinagawa all in about 4 and a half hours (including the ride around the whole Yamanote line)