I took the cheapest flight I could find, used CC points to pay for most of it, and stayed in a hostel with 4 friends, so I managed to keep it pretty cheap. Public transit is fast, reliable, and ubiquitous, but my favorite mode of transportation was, by far, my feet. The food I really wanted to eat mostly came from hole in the wall type places, markets, or the back of a van at 2AM. Most of the sight-seeing I wanted to do was free or fairly cheap (except for the bullet train to/from Kyoto). Picking a neighborhood or two a day with some bullet points you want to hit, but wandering around and between those spots, was what I did, and I thought got a great feel for the different areas. I mean, my gf and I make money, but we're certainly not rich, so trust me when I say that Tokyo can absolutely be done on a budget.
Tokyo was amazing and magical and I ******* loved it. I'm 32 and it was my first real international trip, so I have a lot of other places to see and things to experience. But slamming Japanese beers with my friends on a bullet train from Kyoto to Tokyo on Thanksgiving, getting shithoused on highballs and homemade apple whiskey in a bar the size of my bathroom, eating outrageously fresh sushi for breakfast, seeing a live Pro Wrestling NOAH show at Korakuen Hall--all of it--was just a truly unique experience that I'm going to be chasing for the rest of my life. That is, until I go back. Which I absolutely will.