When travelling in Tokyo, I would highly recommend vending machine Ramen (noodles) for the experience. The ramen is not dispensed by a machine but human contact (read the need to communicate in Japanese) is limited - so may be great for the foreign visitor. The process may look intimidating at first but in reality it couldn't be simpler. Outside the restaurant you will be faced with a vending machine with a selection of buttons, typically you need to select:
1) The size of your noodles
2) The type of noodles
3) Any extras, including egg, extra meat, etc
Simply press your desired buttons (all with pictures on for you to follow), insert money and you will be issued with a coupon. Hand this in to the staff in the 'restaurant' (usually a bar - perfect for single dining) and a few minutes later you will be presented with a piping hot bowl of ramen. Prices are fantastically cheap (no more than GBP5 a bowl) and extremely fresh. As an added bonus, you can feel smug that you've achieved to dine like a local and navigate yourself around what can be a very confusing city.
All around Japan, look for the vending machines with pictures on for a clue