Ramen is cheap and delicious. I'd say it's the most affordable, yet filling and delicious thing you can order in Japan. Ramen is basically noodles in soup. Each ramen place has their own special recipe or broth and they are all delicious. Usually you have a choice of two broths (or a mix of them), and the firmness of your noodles. Generally you order on this big vending machine style thing where you push buttons with pictures of what you want, including extra meat, or noodles or other sides, then bring the receipt to the server.
In one restaurant (that was soooooo delicious) in Kyoto, the eating spaces were these single person cubicles, like study areas. But, if you were a party of two, you could put down the wooden wall between you.
Each region has it's own Ramen style, and each city as well. Okinawa's ramen was really different from Osaka or Kyoto. They had thicker noodles with big chunks of meat and a thin broth. Osaka had a dark, thick soy broth and thin noodles with a choice of pork or beef. Kyoto was just heavenly. I don't even know how to describe the soup, but it wasn't too thick or two thin. I feel like there was some spice, but I can't remember. The noodles were perfect.
Another famous thing you can eat in Osaka is Osaka Sau, which is like a fried noodle cake. It's pretty affordable if you can find a food stand selling it on the street otherwise it's not as good of a deal as Ramen. Osaka also had a lot of barbeque places (a lot), but we only tried one.
In Okinawa, there's a really awesome chicken place with super cheap beer and delicious foods.
Bottom Line: Eating in Japan can be affordable.
Eat Lots of Ramen.