One of the easiest things one can do in Tokyo is eat. Eating in Tokyo is generally cheaper than the average capital of a developed country. Lunch will not cost you more than $10, and you can perfectly dine for less than $15. This does not mean that there are not expensive restaurants. In fact, there are lots of them, and prices can be up to ¥10,000 to ¥15,000 per person. But there are myriads of places in which you can eat cheaply.
An interesting option for lunch is going to a noodle restaurant. There are plenty of them around the main streets and stations. The menu is quite limited (noodles plus vegetables and some meat), but you will not be hungry and it will cost you less than ¥800 to ¥1,000. Generally, all these places provide you with free tap water (generally with ice), and some of them with complimentary green tea.
Don’t be worried with the language barrier. Almost all places exhibit what they offer (including the price) on the front door using plastic reproductions. In case of doubt, you can show the waiter what you want to eat. In several places, this process is even simpler: you pay first on an automated ticket machine and then you deliver your ticket and take a seat.
If you are using the Shinkansen, you can rely on ekiben. Ekiben is a lunch set specially designed to take outdoors. Generally, it will cost fewer than ¥1,000, and it includes what you need for a full meal. You can purchase your ekiben in the shops near the station and take it during your journey (there are no restrictions). In fact, most Japanese do it and avoid purchasing the lunch sets offered in the train, since they tend to offer worse quality than the ones you can buy outside.
Needless to say, Japan is one of the cleanest places on the earth I’ve ever seen. Ekiben boxes, for instance, have "best before" dates that go no longer that the evening they were delivered. Restaurants are usually clean, and they generally cook in front of the customers.
Taking a coffee is expensive for Japanese standards, but not for European. A coffee will cost you between ¥250 and ¥250. It can be the case that a coffee and a cake will cost you the same as a full meal. I suggest going to a café only if you are a coffee addict (in that case, you better go straight to Starbucks), or if you want to see for yourself what the Japanese understand as an "exotic experience."
My advice is to try to avoid as much as possible the usual fast-food stuff. In fact, you will see very few McDonald’s, Pizza Huts, or Kentucky Fried Chickens. These places can be interesting only if you are bored with Japanese food. You will not need them in any other case.