I think it is much popular to eat outside for breakfast in Japan than in Europe. Then, cafes or diners which offer typical Japanese breakfast are rate than which offer western style breakfast.
Then, there is a unique breakast system called MORNING in Japan. Then, Morning has two types. The first one is a menu similar to continental breakfast, you get coffee, toast and boiled egg for a very reasonable price usually under JPY 500. May be you can change the hot beverage to tea instead of coffee. Then, the second one is Nagoya style morning which toast and boiled egg come automatically with your ordered beverage. Then, you have to pay according to the price of the beverage.
The first one and second one sound similar but if you order just coffee at the cafe which offer the first type, you will not get any food. Of course, Morning menu should be expensive than the single coffee but the difference is small. May be the coffee is JPY 400 but the Morning menu is JPY 500.
Nagoya style Morning is spreading rapidly nationwide thanks to Komeda's Coffee, the biggest cafe chain in Nagoya region.