Travel within Tokyo - transportation?

Hi

I will be travelling to Tokyo for 8 days in late May. I will mostly be taking in the sights and exploring Tokyo during the time, but would like to visit Hakone for Gotemba, onsen, Super Autobacs, etc.

I will be @ Sunroute in Shinjuku

What's the best and cheapest transportation to get around Tokyo?
I don't think I will get the JR rail pass as I am not planning to travel between cities.

How long should I spend in Hakone if I wanted to do onsen and shopping? Perhaps one night overnight? Should I join a short tour?

Any help would be appreciated. Thanks in advance!

Think about the Suica and NEX card.
http://www.jreast.co.jp/e/suica-nex/

Hakone you can go by a two day organized tour, see :
http://www.jtb-sunrisetours.jp/JTB.SunriseTours/fronten...

or you can organize by yourself with the help of the Hakone Free Pass at Yen 5000 from/to Shinjuku plus accomodation within Hakone.
Details see under Travel - Hakone in this japan-guide.com

The surisetour does not include Gotemba outlet, so this you will do alone the second day.

The Yamanoto line circles the main area of Tokyo and is run by JR. There are also "special tickets" and you can learn more about these at http://www.japan-guide.com/e/e2017.html

Subways & trains go just about everywhere. And cheap. just keep a train map and a subway map in your backpack. and have fun.

The Tokyo Bus services link up the main rail and Metro stations.. Eg The Bus destination would read "Shibuya Eki" eki= station from say Shibuya to Roppongi Hills of course it shows Roppongi Hills, you get there without having too change (no long walks) and see Tokyo. Cost only 200yen