I second Jason Porath's...go to Yoyogi Park on a Sunday. Take a bento and wander the park, picnic next to whatever bands you like and hang, As it gets to be evening, wander out to Harajuku to see the cosplay girls, and spend some time wandering through Aoyama. My favourite place to eat around there is called the Crayon Cafe, which has good vegetarian options and is all organic. It's next to a market too.
You should also go to Shinjuku station during rush hour on a Friday to see what 7 million people really looks like. When you're eyes are just about popped, head up for some of the famous Tokyo lights. There's so much to do there, good food and good karaoke.
Shibuya/Ebisu has great music too, check out Enjoy! Cafe for great dub (try the Mango Beer, it sounds gross but it's awesome) and good DJs, la.mama for amazing (sometimes all-night) rock, and Bar Shifty for the true genba experience (it's across from the Denny's).