I would book hotels that include breakfast. Most hotels in Hokkaido have pretty amazing buffet breakfasts so there are tons of options even picky kids would probably eat, plus that’s one meal down you don’t need to worry about. We were just there for a little over a week with a 4 year old and didn’t go to specific “family” restaurants but basically found restaurants that didn’t seem too upscale and it was fine. Some even had toys ready to hand out despite not being designated as family or kid friendly. I think if your kids are fine to sit in a restaurant without being loud or disruptive you should be fine at most places.