Mos Burger is the standout burger chain in Japan. There are many others, such as the ubiquitous McDonald’s, as well as Lotteria, Freshness Burger, etc., but none can compare to Mos Burger. It's one of the cheapest places you could hope to eat at in Tokyo, and though it's essentially just a fast-food/burger place, they have just the right amount of original products to set them apart.
The highlight of all of their offerings is the rice burger, which essentially replaces the bun with rice that's been formed into discs. The result is a delicious new take on the burger concept, with a range of available alternatives to the standard meat patty as well. You can get it with pork, fish, vegetables, etc. inside. The only drawback with this is that it tends to fall apart halfway through.
An unexpected aspect of the place is that they have a range of coffee and tea beverages on offer that tend to be quite good in general. One interesting-looking thing I never tried was the green tea latte. I'll be certain to check it out next time I go though.
Finally, onion ring fans will be glad to hear about the oni-pote side, which is a combination of onion rings and fries.
Remember, when specifying size in Japan, there's generally an S, M, and L size, which are read as the letters pronounced in Japanese. Thus, you would say esu, emu, and eru respectively. Don't worry if you forget this - saying "small" or "large" is usually equally as understandable.