Never been to Big Basin at night, I just figured it would be a dark site.

Re Alpine Rd (BTW, it changes name before it gets to Skyline), there's a spot a couple of miles past Skyline, and a couple of miles before the road splits (each half going to the coast), where there is a sweeping right hairpin at a hilltop. There used to be a house there I would have loved to own and build an observatory on. There's room for several cars to pull of the road and a great observing site. But I don't know if it's still dark any more. The road has a lot of curves and lots of deer, drive carefully.
You'll have a clear horizon to E, W and S. N is blocked by the hill, which is that homeowner's private property. Again, keep in mind I haven't been there for over 20 years, there may be MacDonald's on that spot by now.