There are many world class ski resorts with good snow in Japan. One of them is Hakuba in Nagano prefecture. It staged Super-G, down hill, and ski jumping during the 1998 Winter Olympics. It's situated in the Northern Japan Alps. To get to Hakuba from Tokyo, it takes about 4 hours and 35 minutes by highway bus from Shinjuku. For more information about Hakuba, please refer to Hakuba's Website by Tourism Commission of Hakuba
Skiing in Japan can be costly for visitors since food and lift tickets tend to be expensive. Usually, a one-day lift ticket costs from 3,000 yen to 5,000 yen. Ski/snowboard set rentals are often available. If you stay at minshuku (casual Japanese inns), you might be able to save some money. There are many minshuku located around snow resorts.
Resource for Detailed Japanese Snow Resort Information: Snow Japan