While Japan does have some of the best food in the world and the Michelin stars to prove it, eating out doesn't have to break the bank! The trick is to eat like the locals. Here are some general suggestions to find a good cheap meal in Japan.
General Tip: Stay away from International/US Branded places, as they are usually pricier and have different menus than you might be used to.
$3 to $5 Convenience Store or Market - A fresh pastry and coffee from 7/11 is a great way to start the day.
$0 to $10 Hotel - Many business hotels offer a free or cheap breakfast option. Check during booking for details.
$5 to $10 Bakery / Cafes - Bakeries and cafes abound, try the Yamazaki chain for freshly baked pastries at reasonable prices.
$5 to $10 Local Eateries - Follow the suits to find where the local workers grab their quick cheap lunches. Most places will offer set lunches for a reasonable price.
$5 to $10 Fast Food (Japanese Style) - McDonalds is okay, but try the Japanese chains like Yoshinoya (beef bowls) or Mos Burger!
$5 to $10 Convenience Store or Market - Most stores or super markets have a nice selection of pre-made lunch boxes (bento).
$2 to $7 Convenience Store or Market - Those same lunch boxes are marked down after 7pm (varies) to deeply discounted dinners!
$10 to $20 Family Restaurants - Similar to diners, these mid-range eateries usually offer nicely priced dinner sets.
Varies Department Stores - Just like the markets, department store food levels (usually the basement level) discount after 7pm! You can find all sorts of snacks and treats at good prices. They discount because everything is made fresh daily, so if it doesn't sell that day they can't sell it at all.
If you are staying in a hostel or place with a kitchen, ask them where the local market is! Making your own meals and snacks for the day can save a lot of money.
Also, be sure to check out the local "hole-in-the-wall" places; it's usually a great experience and meal. Check with the staff at your lodging or the local Tourist Information Center for their recommendations!
*Prices may vary depending on USD/YEN exchange rate.