Well firstly a Suica card is useful for getting around the Tokyo area, it doesn't save you any money (you charge it up and then your fare is deducted from the balance when you go through station gates) but it means you are not having to use ticket machines all the time and ending up with loads of change. You can also use them on the myriad of private lines in the Tokyo area (they are interchangable with their PASMO card). Getting one is pretty trivial using a vending machine at a station (which has an English option).
What to do depends on what sort of things you are interested in ...
Normal site-seeing, the Sky Tree and Tokyo Tower ... with the former it tends to be best to go very early to avoid the queues. You have places like the Meiji Shrine, the Edo Museum and the museums at Ueno Park as well as areas like Asakusa which are good for a wander around.
If you are interested in anime/manga then you have Akihabara and Nakano Broadway. For electronics the same (you can lose a lot of time in Yodobashi Camera by Akihabara station if you are not careful
)
If you are more fashionable then Shibuya and Harajuku may be more your scene.
Of course depending on budget you could also pick up a 7 day Japan Rail Pass voucher before you go and convert it when you get there (I changed mine at the travel centre at Tokyo station who were very helpful, spoke English and booked our train tickets for us). Then you could go down to Kyoto/Osaka for the day (it's about 2:30-3:00 hours to get there) where the former has a lot of historical things to see. The round trip should almost pay for the pass and you can use it on the JR lines in Tokyo as well.
(mutter want to go back again but probably can't this year
)
edit: Of course if you are there in April then I would suggest checking out the cherry blossom at Ueno park or Shinjuku Gyoen.
