It depends on whether you're on an extended stay for business or tourism or whether you're moving over for the long term.
On my last trip, I was at a Tokyu Stay in a room that had a refrigerator. I didn't like the breakfasts at that particular property--I just took advantage of the refills on coffee---so I went to the nearest depachika and found milk and corn flakes, and snagged a couple of tubes of sugar from the nearest konbini.
If you're moving over for the long term, say several months or more, enjoy exploring your neighborhood. I found myself buying food for different purposes at different places: the mom-and-pop stores for fresh produce and meat, the depachika or konbini for picking up a quick meal on the way home, or the supermarkets for buying staples.
If you're single or going without family members, you may find it more fun and even affordable to eat out at the local mom-and-pop restaurants. You can point to the plastic models of food or the picture menus.
As with restaurants, where the abundance of eateries forces one to ask the question, "Where should I not eat?" the abundance of options for food shopping lead to the question, "Where should I not buy groceries on this occasion?"