There are a few roads that go west into the mountains between Hecla Junction and BV. Take one of them into the National Forest and you will find plenty of unimproved spots to park and camp. No water sources to speak of though so byob. There is also the Chalk Creek drainage but there will be plenty of others wanting to share your spot.
Take one of those roads that Don mentioned, then backpack in about 15 miles (don't forget your snowshoes!) and you may be able to avoid the Memorial Day crowds. But seriously, try up in Mushroom Gulch off US 24 toward Trout Creek Pass.
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