When I was there for extended work, I didn't take advantage and go outside of Tokyo very often. I usually spent my day in the office and found someplace for dinner and a drink in Shinjuku after work. I usually spent a lot of the weekends just walking through various districts. Harajuku is certainly a place you want to go just to people watch. Shibuya has a lot of streets and alleys with lots of interesting stores as well as you can go over to Yoyogi park where there are a lot of street musicians.
I tend to like to find bars or clubs with live music when I travel, usually, jazz but also rock or pop is ok. Tokyo had lots of it so just had to take the chance to go in and try to talk to people which can sometimes be an issue, even with the bartender.
Most of my trips outside Tokyo were usually just an overnight trip to visit hot springs. Kyoto is beautiful but probably not great for pop culture. I never made it up north but friends are planning to go in December to Ski so may get my chance.
If you make it to an Onsen though you can not be shy.