You will probably hear many stories about the high prices that would put anyone off going to Tokyo.
I used to live and work in the area for a few years and found it more affordable than London, and Sydney (my hometown).
There are a few rules you should follow, to keep in budget:
1. Never take a taxi unless you absolutely need to
2. Avoid the bus night tours of Tokyo - they take you to two or three locations you could just as easily get to on the subway
3. Eat out where the locals eat out. It can be a little daunting when it comes to the natural shyness of the locals and language difficulties, but the food is authentic and you save your Yen. After a few beers, you seem to find that everyone speaks your language. :)
Tokyo is a contradictory world of ancient tradition, discipline, state-of-the-art electronics, and the birthplace of Pokemon. Visit Shinjuku at night for the blade runner-esque atmosphere of neon lights, Ikebukuro for the view of Tokyo from the Sunshine City building, Shibuya for the giant TV screens at the pedestrian crossing outside the station, Ginza for the window shopping, Ueno for Ameyoko (a huge shopping area with a lot of bargains).
If you are an early riser head for the Tsukiji fish markets at dawn to watch the fish hawl from the four corners of the globe and the subsequent frenetic auctioneering taking place.
Tokyo also has some beautiful parks and gardens - my favourites were Rikugi-en, Shinjuku gyo-en, and the Imperial Palace Gardens.