Greater Tokyo Area
The Greater Tokyo Area is usually called the Kanto (関東) area and includes all areas surrounding Tokyo as in the map below. However, for tourist purposes the areas of Gunma, Tochigi, Ibaraki and Chiba are treated separately by “When Japan” due to their relative remoteness and lack of convenient tourist spots. The three regions remaining are Tokyo itself, and then Saitama to the north and Kanagawa to the south. This trio is far more directly connected to Tokyo by public transport and contain the bulk of the places of interest to tourists. As transport is a key factor in how you travel around in Japan, “When Japan” splits the traditional Kanto region up further.

Tokyo
Of course you are going to Tokyo on your first visit to Japan, if only because your flight will almost certainly land there. Check out the main Tokyo article for strategies to making the most of your time. Focus on places and activities that can only be experienced in Tokyo and get out as much as possible, budget allowed.
Saitama

If you type in Japanese “埼玉って” (when you say Saitama….) into Google a meme pages appears in Japanese with some maps of people’s opinion of the various areas of Saitama. The one that has the words “boring” in the center is the best fit. Saitama is mostly a commuting town with fast and direct links into Tokyo, with the more northern areas a mix of semi-countryside and industrial areas with large warehouses. There is very little reason to go there even for Japanese however a few places are worth a visit. Check out the main article for more details.
Kanawaga

Kanagawa contains the well-known cities of Yokohama and Kamakura but also extends all the way to the hot-springs resort area of Hakone, close to Mount Fuji. Despite it’s more rural identity (certainly compared to Saitama), much of the prefecture is low-rise residential housing interspersed with rice paddies and the occasional large factory. Outside of the famous locations of Yokohama, Kamakura, Hakone and Kawasaki, there isn’t much else that draws foreigner tourists, although the numerous large festivals that take place at various locations throughout the year are worth looking out for.