Hi EJ. I live a few miles from the park HQ and have done all the trails there ad naseum.
As mentioned above, the standard day hike is from the park Headquarters to berry falls and back. Standard can mean tons of tourists on weekends. But it is famous for a reason. Alternately you can keep going and hike all the way to the ocean (12 miles) and Waddell beach where someone could pick you up, or where it is possible to then take two buses (connecting in Santa Cruz) back to the park. Just make sure you know the schedule.
Two alternate routes back from Berry falls are the Howard King trail and Sunset trail. The former is my usual route if I want to get away from the tourists - almost no one goes that way. There is a nice bench when you get to the ridge with some good views down the east Waddell creek gorge towards a the sea. There is an area on Howard King almost at the top, but not quite, which is like Western Garter Snake Eden, where I always see a ton of them, but I assume there are other relatively undisturbed parts of the park that might have the same.
Alternately you could start at Waddell beach and round-trip to the falls, or as far as you want to go, from the opposite direction.
As for overnights, there really isn't much of a typical 2 day trip, except perhaps out and back. Nothing in the Santa Cruz mountain is real wilderness, and if you hike for a good part of a day in any direction you will be back to civilization. You can camp at one site on that route, with reservations only (there is nothing that doesn't require reservations not anywhere on the peninsula). Alder is the campground that is usually used, several miles for the sea. There are a couple of other campgrounds on that route perpetually "closed for restoration" though I haven't checked their status in a number of years.
A far as the 'natural history' the area nearer the ocean, where the valley widens out is very interesting. That is where Alder campground is. One time when I was there overnight I heard 5 or 6 different great horned owls, each with a different unique call, hooting at each other from around the valley for hours. It was quite beautiful and magical.
If you are ambitious you could, after an overnight, hike back to the park HQ using the Clark connection via chalk mountain. Bring a map. You will get a "high" view of the park that way with distant vistas, and at chalk mountain (remains of on of the n ancient coastal reefs), a good view down towards the coast above Ano Nuevo (where the elephant seals bask in their squalid glory for part of the year).