I know Hakuba in Nagano or Niseko in Hokkaido is popular ski place for foreigners.
However, I recommend you to visit Zao in Yamagata, where is great place to do ski and sightseeing.
Especially, around Ice Monsters(Juhyo) festival season, end of January to first of Febuary is the best to visit.
“One of the natural wonders at Zao can be found at the top of the mountain during the coldest months, usually from December to February.
Super cold snow, combined with seasonal winds, encapsulate the mountain’s trees forming unique shapes locally known as “Juhyo” also known as “Ice Monsters”. This spectacle can be also fully appreciated during the night illuminations at the top of the mountain during the high seasons.”
by Yamagata City and Zao Hot Springs association (http://www.zao-spa.or.jp/english/ski.html)
I did ski there and that was great experience.
Condition of snow was perfect and did ski around Juhyo was so romantic.
After doing ski, taking hot spring bath for warming up cold body is real charm.
Also you would have great experience to have soba at local restaurant in Yamagata.
Some restaurants have kept traditional style.
You might be surprised that customers sit straight on the Tatami floor and share long table with others.
Taste of hand made soba is so special and fresh. You exactly feel Yamagata’s soba is superior.
2h 30 min from JR Tokyo station to JR Yamagata Station by JR Yamagata bullet train, Tsubasa.
and around 50 min from JR Yamagata Station to Zao-onsen by bus.