I'm in Concord as well. Went out this morning, took a friends 12 year old out for her first bird. The fun started when I was showing her how to clean the Tom.
74 yard neck shot, what a champ!
OK- BLM lands are accessible, but best with 4-wheel drive; Knoxville Rec outside of Berryessa. Lots of pressure out there though. I've heard birds out there, but the fires have probably knocked their numbers back quite a bit.
Going East, the Sierra's have birds, but try to stay below 4,000'. You'll have to drive a lot, listen even more. I've hunted the Auburn SRA, some birds there, but again a lot of pressure. I prefer AWD for access, but I've seen Honda Civics out there.
CA DFG has draws before every season for SHARE hunts- if you're licensed, you should be getting emails with the reminders to apply. Lot's of opportunities there.
All around Concord- Walnut Creek, Martinez, Clayton and the land around the levee's, have area's that are unincorporated and legal for hunting, with the owner's permission.
That is really your best bet- Use ONX maps or what ever app that you prefer to find out who owns the land and start a relationship with them for access. It's a little work, but the friendships you'll create and access to excellent properties is worth effort!