Henry Cowell is great - and is easily accessible. The nature trail by the Visitors center is really nice. If you have more time and want to drive up the mountain a bit, Big Basin is also a really nice park. It's got some great hikes - and also a short nature trail for those who want to be out in the redwoods, but not do an actual hike.
Those would be my top choices.
Agree with NM. Just getting to Big Basin state park is pretty winding and for some (well a lot in my experience) it can cause car sickness. If one gets to Henry Cowell by Hwy 17 and then to Felton, it is a relatively easy drive (well less winding)
If you want to visit Henry Cowell there is no reason to use Hwy 17. Just stay on Hwy 1 and in Santa Cruz, after the hairpin curve in the freeway you should be in the right lane and take the first exit (it happens right away) and you will very shortly come to a major intersection. It is labeled Boulder Creek or Big Basin This is Hwy 9. Seven miles later Henry Cowell is on the right side, on the outskirts of Felton.
There is an interpretive trail of almost a mile. Pick up a brochure at the visitor's center. Big Basin is wonderful but much larger and getting there is as belomiser describes. I would not attempt it without having half a day to devote to it.
Thank you so much for the help
Very helpful info--car sickness could be an issue with me!
Many thanks for the help.