How about ”Teishoku(a set meal)” restaurants?
I think there are many Japanese people working in Shibuya eating at Teishoku restaurants during lunch time.
It is a casual dining room.
Theses restaurants look good.
If you like sake, Sanchokuya Taka is the place to go! The place which allows only visitors with reservations has no menu. Customers tell the budget and the chef will cook the food that best match with that day's sake. The official website in Japanese says that the budget is about ¥8,000 ~ ¥15,000
Here is the link to yelp.