With over 500 resorts, you're never really that far from the slopes in Japan.  While the previously mentioned regions are probably the most well-known and popular resort regions, there are countless other resorts dotted around the Japanese mountains.  Here are some of the other notable regions:

Gunma Prefecture
Tenjindaira Tanigawake and the resorts around Minakami are easily accessible from Tokyo, as well as the Manza Onsen and Kusatsu areas.

Nagano Prefecture
Togakushi and Iizuna resorts are located in close proximity to Nagano City. Shirakaba-ko, Kurumayama and Tateshina areas near Lake Suwa in southern Nagano have some small resorts that are conveniently located from both Tokyo and Nagoya.

Toyama Prefecture
Resorts south of Toyama City.

Ishikawa Prefecture
The area around Hakusan and Kanazawa has several ski areas including Kanazawa Seymour, which features some challenging terrain.

Yamanashi Prefecture
Fuji Tenjinayama is where you can ski in the shadow of Mt. Fuji, and if traffic is thin it is only 90 minutes from Tokyo.

Gifu Prefecture
The areas around and to the north of Mount Washigatake. This area is popular with young people from Nagoya and Osaka.  Dynaland is also a good choice for people coming from Nagoya.

Shiga Prefecture
The area around Biwako Lake.

Tottori Prefecture
Daisen is an popular destination for people in Kansai.

Hyogo Prefecture
Areas around Mount Hyonosan.

Hiroshima & Shimane Prefectures
Areas north of Hiroshima (Hiroshima Prefecture, Shimane Prefecture)