club ageHA is a great club. Kind of far though but there is a shuttle bus that takes you back at night.
clubs/pubs in the roppongi area as it's the foreigner district. Club Feria was great, it was packed to the max when i was there. clubs don't get busy until about 1AM. Club Womb is bumping too.
as for food, almost everywhere i went was great for food. stay away from the kill bill restaraunt in roppongi though.
if you can, try to get reservations for sushi yasuda (also in roppongi area)
SUSHI BAR YASUDA
shibuya is a big shopping disctrict and harajuku is north east from there (about 15-20 minute walk from the famous 109 crossing)
shinjuku is another place you can shop but also has red light district. Go see the robot restaraunt show. Words can't describe it.. get a flyer from a hotel and you save $10 or something.. it's kind of pricey about $50/person
3 weeks in tokyo is a long time.. i spent about 10 days in tokyo and 1 week in kyoto/osaka