Osaka (higobashi)This is not a great area for supermarkets, I believe I remember there being one in the area, but I can't
remember where. You will find many conveinence stores, but they will be more expensive and do not discount.
The best area for supermarkets is in south Osaka. One of the biggest is MaxValu in Namba, if you go
there late in the evening (after 8.00 pm) fresh foods will be discounted to clear (bento boxes,
sandwiches, sushi, etc). If your hotel room has a fridge you should be okay keeping stuff for the next day:
http://g.co/maps/z94tvThere is also a fairly new supermarket within the JR Namba station building just north of Max Valu, but I thought it to be rather expensive.
Also look out for Tamade supermarkets, this one is next to Exit 1 of Hanazonocho subway station:
http://g.co/maps/wyz5tAnd I am pretty sure there's another supermarket at exit 3B of the same station.
Hiroshima (kanayamacho)Directly east, and on the far side of Hijiyama Park should be a MaxValu, even though the store says "Saty" on Google StreetView.
http://g.co/maps/xmx34Kyoto (karasuma), Kyoto (gojo)These are practically next to each other, Gojo is not great for supermarkets, but if you go west of Karasuma station, there are a few to be found. Next to Shijoomiya and close to Omiya station is a Frescso supermarket:
http://g.co/maps/zur7fContinuing west on Shijo Dori there is a Gourmet City:
http://g.co/maps/xaaynThere is a Coop supermarket near to Nijo subway and JR stations:
http://g.co/maps/qj5xa