Congratulations on finally managing the trip. I hope you have fun. I know of some people who have gone to Tokyo and some nice, discount places.
I've heard of this place, a hostel, by the name of
K's House Tokyo. I've heard good things about it, and since you're by yourself, you should get a decent rate. I think it was about ￥3000 for a room with one bed.
Another place I was told was nice was
Sakura Hotel, and I think the rates were reasonable there as well.
I was also informed of the
Tokyo Inn hotels, which are all over, have decent service and prices too.
Oh, and here's something that should help you once there. It is called
Hyperdia, which "is an online timetable calculator for the Japanese transport network."
I hope these help some.
As for taxis, I always heard that they were expensive and that it's encouraged to avoid them and to rely on the other forms of public transit. I know that the hostel place I mentioned above is right next to a railway line.
I can't help you too much since I don't know of how much cash you should have for such a trip. Hopefully, someone who's visited can help there.