Been to the skytree, if you get there on a clear day you might have views all the way to Mt. Fuji, hazy day and you can't see as far, still quite good though, but a bit boring very quickly.
Go to Shibuya, busiest crossing in the world, lots of independent shops you can wander around in.
Harujuku is awesome, Takeashita Street is really busy and lots of good shops, also a temple that you can go to.
Akihabara has loads of technology and anime shops, if you go on a sunday there the roads are closed so its pedestrian only and there is a market.
Asakusa has a huge Buddist temple with a market leading up to it, its a beautiful place to go to, definitely a must see.
Tokyo Decks has an indoor amusement centre, lots of virtual games and an indoor roller-coaster, and there is a huge mall with loads of fantastic restaurants to choose from.
I was with scouts when we were in Tokyo and managed to do all this (and more, but they were one off events), hopefully you'll be able to see some of this!