I would budget 3000 a day for food -- you might have an extra cushion that way, or you might have a cooking emergency where you need to buy a pot or something. Also, this is stupid, but you should have three days of drinking water and a few "pantry" items to last for three days just in case there's an earthquake or typhoon. Better safe than sorry. You can drink it all up the last week if you buy the 500 ml bottles (approx 100 yen each -- although you can get it at Costco much cheaper if you have access to Costco). Say, 1200 yen for the water, 500 yen for three cups of instant ramen, 500 yen for three cans of various fish, 500 yen for three to five cans of fruit, and 500 yen for a couple of boxes of crackers. You'll be hungry, but you won't starve.
If you were staying in a hotel, I would expect the hotel to kind of take care of you (if only to clean out their giant freezers of food). But if you are on your own, it wouldn't be a bad idea to plan for the worst case.