Alcohol is cheap compared to the prices in Australia, so drink your hearts out. You especially have to dive into Japanese whiskey if you're into whiskey, because that stuff is meeeeega expensive outside of Japan.
Food is relatively cheap as well, but barbecue places will usually run you about $30-50 per person.
If you just need a list of places to go around/nearish Tokyo, check out;
Akihabara - Lots of electronics and anime/manga goodies if you're into that kind of thing
Asakusa - Very 'traditional' Japanese place with a biig temple to see
Harajuku - Umm, quite a trendy place for youngsters, lots of clothes shops and such, there are also temples/shrines near by
Shinjuku - Shopping and close to nightlife/red-light district at kabukicho
Shibuya - Shopping
Ikebukuro - More shopping, kind of like Akihabara
Odaiba - Toyota car show and some more shops, a very modern place
Roppongi - Nightlife/red-light district
Ginza - Heaps of boutique stores, and don't forget to visit the Tsukiji Fish Market close by, you have to try sushi there
Well, I've probably missed a lot of stuff, but those were some of the places I visited and revisited during my two week stay in Tokyo a while back.
Since you have three weeks, you should be able to travel outside Tokyo if you somehow run out of things to do! I think you should visit Osaka as well, it's only a ~3 hour train ride away.