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Sierra Nevada College, I think they have a separate campus in Tahoe but there main campus is just over the border in Nevada. They have a pretty reputable ski team and are located extremely close to Tahoe.
Sierra Nevada is located in Incline Village Nv. About three block form the lake (tahoe) Not California but as close to the skiing as you can get. Not too many close. Cal State Sacramento is about 2 hrs from Tahoe. University of Redlands is about 45min to big bear not amazing skiing but closer.