You’ve gotten some good answers but I’ll add my ¥20.
You could knock most of your initial question out with a visit (or two) to Shibuya.
The Tower Records there is my all time favorite. 6 floors and I’ve only ever made it to the 2nd. First floor has lots of listening stations and 2nd floor has most types of J-* music that you might be looking for. Anything above 2 is mostly imports which means that you’ll likely be able to get it cheaper at home. CDs in Japan are expensive so you really have to want them.
There are a few other shops in Shibuya that carry new and used where you can find some music at a reasonable price. Cisco comes to mind.
If you’re into the whole Shibuya-kei thing then you might also want to check out the HMV in Shibuya since that seems to be one of the original epicenters of the movement.
Food is everywhere in Shibuya. What am I talking about, it’s everywhere in Japan. People are obsessed with all aspects of eating so it’s difficult (not impossible) to have a bad meal. I love Shibuya for their ramen shops and one of my all time favorite udon restaurants can be found there as well.
If you’re looking for urban vinyl depending on how determined you are, you might want to pick up a book called Tokyo Underground covering toy and design culture in Tokyo. The book covers some urban vinyl shops and a lot of Japanese toy shops so it might not be exactly what you’re looking for. A lot of these places can kind of be kind of out of the way but it could be a good adventure.
If you’re a rockabilly chick you must go to Yoyogi Park near the Harajuku JR station on Sunday to check out the Tokyo Rockabilly Club. I’m sure you’ll make some new friends.
Akihabara (aka Akiba) is another good destination for electronics, toys, cheap eats and general otaku (geek) culture. Check out the Yodobashi camera while you’re there. The 6th floor (I think that’s the one) has lots of toys and some urban vinyl. The top floor has some pretty decent restaurants. If you’re looking for some inexpensive sushi there’s a decent kaiten (sushi belt) restaurant that’s known for their tuna.
If you want culture go to Kyoto :).
Have a great trip