When we're traveling we like to get something quick, inexpensive, and most importantly delicious for breakfast. It's also fun to try something we've never had before.
When staying at a Ryokan (Japanese inn), or Minshuku (bed & breakfast) it's worthwhile to get breakfast if it's offered. The food usually comes in many small dishes, and the contents of these dishes varies from lodging to lodging and region to region. If there's something you can't figure out how to eat you can always ask your hosts 「これの食べ方はどうですか。」- "How is this eaten?". When you are done, don't forget to tell them - 「ごちそうさまでした」- "It was a feast".
Self-serve bakeries are another good place to get a quick breakfast. These shops are often near train stations, and usually don't have a place for you to sit and eat. If they do have a seating area and you wish to use it, you are sometimes expected to buy a beverage. You will know this because they will ask you 「お飲み物は…」- "and to drink...?" At the entrance there will be a stack of trays and a box of tongs. Grab a tray and tongs, then select what ever looks good to you. メロンパン - Melon bread and あんパン - buns stuffed with sweet bean paste are always good. For something more heartier you can get ウイナー - pup in a blanket.
If you don't mind your bread a little stale, you can sometimes get a big discount before the store closes. This usually takes place around 22:00. You can tell something is up because people start crowding around but nobody's buying anything. Then the signs come out reading 「30%OFFタイムサービス」or「三割引」and it's a mad dash for the best pastries. Both of these mean 30% discount. 割引 is a 10% discount, so 三割引 means 30% discount.
There's a chain of restaurants that I like called Yayoiken. All their breakfasts are under ¥500. They are typical Japanese light breakfasts usually consisting of some combination of fish, rice, natto, miso shiru, or (this always shocks foreigners), green salad.
Check out their breakfast menu under the 朝食 heading.
They are located in most major cities.
You first pay for your meal at a 食券 販売機（しょっけんはんばいき）- a meal ticket vending machine inside the restaurant. I can't recall whether or not the machine had pictures or words. I usually keep my dictionary handy in either case. You can buy your drink at the counter.
Unless you are going an a major hike first thing in the morning, you don't want fill up too much because there are always opportunities along the way for tourists to purchase and taste the 名物 - local specialities along the way.