Try Lake Alpine, just east of Bear Valley ski area on Highway 4. You'll need a SnoPark pass, and you'll park just about at the road closure before Ebbetts Pass.
Though this is a popular area for snowmobilers, a) they leave as the sun sets, b) they're not along where you'd be camping, and c) it's not too difficult to get to the Carson-Iceburg Wilderness. There's some absolutely lovely scenery in the area.
From the parking area, it's about 1/4 mile or so to the first reasonable camping location, about 1 1/2 miles to another, and then another mile or so to the wilderness boundary.