Answering Patrick's question "Are any permits needed for any part of that trail? The one from Palo Alto to Santa Cruz."
No permits are needed. However, all of our camping on that trip (and the other interesting Bay Area hikes we've done) are stealth camping trips. It's not hard to find good stealth campsites, and in our experience the rangers don't care as long as you use a "don't ask don't tell" policy and follow normal stealth procedures (set up after sunset, break camp early, not in view of roads or buildings or "legal" campsites, no fires, no noise). We only stealth camp on public land, not on private land.
We've taken three good trips that started or ended in Santa Cruz, any of them would be great "avoid the holiday traffic" July 4th options.
San Francisco to Santa Cruz via the coast
Palo Alto to Santa Cruz through the Santa Cruz mountains
Santa Cruz to Monterey along the beach
Route details on all of those are in the photo galleries: http://amyl.smugmug.com/Backpacking/BayArea
I'm a big fan of taking advantage of the fact that we live in the best urban area in the US (maybe the world?) for backpacking out your back door. We have a terrific network of trails, the only downside is that it really requires stealth camping. Not hard for seasoned hikers to stealth camp, but a little intimidating for beginners. If you've got questions about any of those routes, or others we've taken in the Bay Area, send me a PM.
Amy, Palo Alto