To help you understand those words I will give you few examples :
地区 : Those are districts/wards in a city, there are for example 23 special wards in Tokyo. ( Shinjuku, Shibuya etc ...) http://en.wikipedia.org/wiki/Special_wards_of_Tokyo
You will say 新宿区 (the ward of shinjuku) 渋谷区(the ward of shibuya). In every japanese city you have 地区
地方 is a region like Kanto or Kansai, it is the word for an administrative region.
地域 is a general word for the term " a region", it could be the asion region, the oceanian region, north of USA, north america ...
地帯 and 区域 definition and nuances you gave are accurate and pretty clear :
地帯 = area; zone; belt (of land)
区域 = limits; boundary; domain; zone; sphere; territory
Edit : As the Author asked about more details, here they are :
First japanese is about kanji :
in 地区, you have :
地 : earth, soil, ground
区 : area, district, region, ward ( like 新宿区, 渋谷区 )
so for a ward you will use : 地区
for a city I don't think you can use this form
for a prefecture you will use 地市
for a region you will use : 地方( example : 関東地方 )
All those word are talking about the area, the soils of those places.
So it means in your roman, the author is considering 西東京 as a fictional special ward of tokyo and then calling it 西東京地区.
About the word 地帯 and 地域
帯 : the main meaning of this kanji is a belt.
地帯 : is what is written up there, an area, a zone, a belt of land, for example : サンベルト地帯 ( the sunbelt in USA ). Indeed, a belt of land is a zone, and is an area. The meaning is a belt of land, but it can be translated into those 3 words depending on context, that's why you gotta think about Kanjis, and not about translators.
域 : level, limits, range, region, stage.
地域 : I let you think about the meaning of this word, it can describe anything. ( the most general word to speak about "a region" of the world, of a country, of a anything ).