I'm sorry, but that was hilarious
There's no such thing as a cheap place to stay in Tokyo. Your vest bet would either be a so called "love hotel" (which provides a rather weird place to stay), capsule hotel (not a good idea if you're claustrophobic, though) or stay with someone you know.
As for things to do, get lost in Shinjuku. Go see Shibuya at night and laugh at akiba in Akihabara and buy electronics taxfree. No haggling, though. Asakusa is very touristic, but also a must and the best place to get a yukata and kitschy souvenirs.The Edo-Tokyo museum is rather good. And you want to go to one of the less known places as well. I lived near Tachikawa, which I loved for the futuristic atmosphere. Kichijouji was always fun because of all the cramped stores. I'm sure there are better places than that, but I just happened to live near there.
You want to get a subway or train pass of some sort, because they're gonna be your main form of transport.
Oh, and as soon as you arrive, try to get a ticket for a Kabuki play. It's expensive and impossible to understand, but a really special experience.
Can't think of any more stuff right now. Maybe later.