Donki is the most famous discount store chain in Japan. Donki has all sorts of stuff, from snacks, cosmetics, electronics, clothes, etc. Many tourists like to shop at Donki. Donki is also a TAX-FREE store which is another good point.
Ameya Yokocho is a very famous reasonable place to shop. There are not only Japanese shops but international. Moreover, there are more foreign shops, compare to Japanese, however, you will never get bold there. http://www.ameyoko.net/
And also, Jujo Ginza is also a good place to visit if you are looking for the reasonable shopping. http://jujo-ginza.com/en/