We'd recommend driving most of the way up to the Observatory, parking on the side of the street before you get to the top, then walking the rest of the way up. The Observatory is beautiful to walk around, there are great views of the city, and you can continue a hike up to a lookout point for even better views.
If you're queer, look up Ginger Rogers State Beach in Google Maps. If you're not, Ginger Rogers is still fun, but you might want to look up Will Rogers State Beach instead.