Butano is nice, we've taken our kids there, but I wouldn't call it backcountry. Point Reyes can be fun, though its probably full for this weekend.
There's also some bp'ing opportunities at Armstrong State Park (north, near Guerneville. won't be nearly as crowded as Big Basin trails).
Of course, if you have time to drive, 3 hours away is Emigrant Wilderness. Its a good place for early season Sierra adventures. No ticks, and at least last weekend when we were there, no mosquitoes above 8000 feet.