Like KeoRS suggested, definitely the New York bar at Shinjuku Park Hyatt. Order Yamazaki 18 and enjoy the view
Tokyo Tower in Roppongi. The Sky Tree is still not open yet I think.
If you have time for a day trip, go to Kamakura. Its about 60 min by train if I remember correctly. A little past Yokohama. It will be beautiful this time of year with the leaves changing colours. Lots of temples and a view of the ocean from the hill tops.
Try to find Harajuku Gyoza. Its off of Omotesando near the Bvlgari and Maison Martin Margiela stores. It will have a line up probanly but the gyoza are delicious and cheap. I also suggest the moyashi bowl.
Tokyo is one of the greatest cities in the world, enjoy your stay
