I found lots of combini (conv stores) all over the parts of Kyushu I toured..... except off in the mountains and various stretches of coast where all the towns and villages are really small. Combini were great for lunch. But at dinner I almost always ate out somewhere, for the experience. As mentioned by others, I could see making dinner from combini offerings.

On google maps you can search for "convenience store" and see where they show up. Family Mart, Lawson, 7-11 are good. (The results also show gas stations, and I have no idea what they offer.)

I was staying in inns, cheap hotels, air bnb, etc.