Dante-

Three shops come to mind right off the start.

Old West Gun Room
oldwestgunroom.com
3509 Carlson Blvd
El Cerrito, CA 94530
(510) 525-5329

Contra Costa Collectible and Firearms
1429 Cypress Street, Walnut Creek
925-937-3376

Sportsmans Access
3125 Penryn Rd
Penryn, CA 95663
916-652-2220

Old West and Contra Costa Collectibles are both quite near San Francisco. Travel time from Davis is about an hour. You should call in advance in order to make sure they'll have double rifles in stock if that is specifically the only thing that you want to see, otherwise these two shops are good to visit anyway as there is always unique and interesting stock you won't find elsewhere.

The third shop I noted, Sportsmans Access, is a well established broker of very high grade double rifles and shotguns, as well as other forms of high grade sporting arms.
Tyler Jones, the owner of the operation, has moved some of the most significant and valuable firearms to come through the state, things such as best grade Purdey game gun pairs and 700NE double rifles.
This shop is a bit of a drive from SF, budget at least two hours in the car from downtown San Francisco to this shop, but I assure you the drive is worth the time.
Travel time from Davis is just under an hour.

While you're out in that part of the state, check out Huntingtons in Oroville, one of the West Coast's most established and trusted sources for reloading supplies and sporting equipment.
While you're there check out the amazing collection of historically significant guns and hunting gear in the back of the shop.

Huntington's
huntingtons.com
601 Oro Dam Blvd. East
Oroville, CA 95965, USA
Phone - 530-534-1210
Toll Free - 1-866-735-6237

Feel free to contact me when you get out this way, I might be interested in joining you for the trip to Tyler's place if you elect to go that route. Same applies to Old West and Contra Costa Collectible.
If you have any more time to goof off while you're out here, drop me a note and let's see if I have time to arrange a day at the ranch shooting doubles, clays, or just blasting steel with the big bore pistols.

Any way it goes, I hope you enjoy your visit to California.
Let me know if I'll be able to help you find what you're looking for when you get out here.

--Tinker