For visitors coming to Tokyo that want to know where they can try different foods on a budget.
Convenience Stores (Conbini in Japanese)
They are all over the city and offer a number of quick food items that are cycled out daily. So you can find everything from sandwiches, salads, and ready made meals. If they need to be heated up, the cashier will always ask you if you want it heated up.
The workers at the stores may or may not speak English, but the workers are typically very helpful and polite. So just don't worry about it too much because you can typically use gestures and point to things to work it out. Just smile and enjoy the experience.
One thing I recommend visitors to try is the rice balls/trianges (onigiri). The most popular is probably the tuna & mayo or Salmon. Some have sour plums (called umeboshi) which can be a shock to the uninitiated.
In the colder months, you can find a lot of stores selling oden which are a number of ingredients such as boiled eggs, fish cakes, meat on a stick (yakitori) in a mild soy-flavored dashi broth.
Next the registers at most convenience stores, you find hot foods such as fried chicken patties (Lawson spicy is good), meat on a stick, hot Chinese buns (nikuman), and a variety of other things. Usually these foods haven't been sitting there long (depending on how active the store is) but you can just look to see what looks good to try.
All of these foods are really cheap to try and so if you get something you don't like then just dispose of it discretely because most Japanese typically don't like to waste foods. So please be mindful to not be spiting things out, walking while eating or openly throwing away a number of things with Japanese friends. They will be a little shocked and you'll get a lot of stares.
Here is a list of the top convenience stores that you can visit. Open them in Chrome and use the translator to navigate around to see all the unique things they offer
7-Eleven - http://www.sej.co.jp (also has atms that work with international cards)
Lawson - http://www.lawson.co.jp
Family Mart - http://www.family.co.jp
Circle K/Sunkus - http://www.circleksunkus.jp
Ministop - http://www.ministop.co.jp