I know there was a place that sold reasonable backpacks on アメ横／あめよこ* near 上野駅／うえのえき. Maybe not $20, but same vicinity. Don't remember where it was well enough to draw it on Google Maps, though. It's a fun area to browse around in if you haven't been there, lots of interesting shops, some reasonable 回転寿司／かいてんずし/rotation sushi, an international grocery in a basement that's the only place in Japan I found root beer for sale...

* For clarity, アメ横 is a shopping street.