I think it is not common to eat breakfast outside in most of the European countries, especially Czech Republic which I live. On the other hand, it is very common for US citizens to eat outside in the morning.
Japanese eat at home but there are certain population which eat outside regularly. Then, there are several places where you can eat for breakfast. Then, it is much common to have western style breakfast rather than Japanese style breakfast if you eat outside.
Many bakeries have place where you can sit and eat after paying the bill. Then, restaurant called FAMILY restaurant also serve breakfast(they also serve traditional Japanese breakfast too). The last place is the cafe. Cafe is divided into self service style which you order and pay first or full service which you have to pay when you leave. Self service one is common in Europe too but full service cafe in Japan has a different system than in Europe.
There is a system called MORNING. It is usually valid from the opening to 10:00 or even to noon. When you order a drink, it comes with a toast and boiled egg. Or even something else too. Then, you have to pay just for the beverage. Morning system started in Aichi prefecture where eat outside for breakfast is very common and there was a fierce local battle to gain the customers. Then, this system spread to nationwide.
On the other hand, FAMILY restaurants do not offer MORNING system but usually the meal comes with unlimited consumption of drinks(hot and cold). Which means you do not have to pay for any extra drinks which are mentioned in the offer.
Which one will you take? Have a quality beverage with free toast and boiled egg or quality meal with free drinks. If you want to stay longer, choose the FAMILY RESTAURANT!