Good place to live?

I want to know what places are there to move in Tokyo that are affordable and monthly rent is less than 100,000. I'm thinking about the Shinjuku and Shibuya wards. Any help would be nice.
Also I have another question. How far are Shinjuku and Shibuya from one another.

Shinjuku and Shibuya station are 7 minutes from each other on the Yamanote line.

They are two of the more expensive wards to live in although Shinjuku in particular has cheaper areas. You would be most likely to find a small apartment under 100,000 somewhere on the Oedo line- Ushigome Yanagicho or Wakamatsu Kawada for example. These are both in Shinjuku ward but are less expensive areas. The older the building and the further from a station the cheaper it will be.

Just a little further out (5 minutes from Shinjuku station) is Nakano ward- prices start to drop sharply here and you might find 1DKs for 80,000 or less.