Are you trying to get into NorCal or SoCal? Why do you want to be in CA?
I was in your situation in law school - similar grades, type of school, etc. I struggled in 2L OCI in NorCal, but did fine on the East Coast. I took the sole offer I got from NorCal to get California on my resume. After getting that (well-regarded) firm on my resume, taking the bar, and doing a CA clerkship - I got offers from all the other Bay Area firms I was interested (who had rejected me as a 2L, likely for geographic reasons), and I got to pick my top choice. Even in that second round of firm interviewing, I got grilled on "Why California?" - but less critically. Now, as a diehard adopted Bay Arean, I wish it wasn't so hard for East Coasters to get into this market. It's an *amazing* place to live and work.
For someone like you, who clearly has the credentials to be hired, they'll be listening for two things:
- Are you serious about being in CA this summer? Or, are you looking for a free trip over flyout week? Will you take a CA offer over a NY/DC/BOS offer?
- Are you serious about relocating to CA for good? Or, are you planning to come out for a couple years before "settling down" on the East Coast, "needing to be closer to family" (or whatever it is East Coast defectors from CA do...

)
So, tips:
- Have a solid "Why California?" narrative; run it by CA friends beforehand if possible. Sound enthusiastic about CA, absolutely committed to the idea of working there indefinitely, and non-defensive but firm that you're secure in your decision to move.
- Emphasize if you're into a type of work that's disproportionately in CA - e.g. patent-related
- Consider mentioning any "unofficial" ties to the area that will cause the interviewer to be able to picture you wanting to stay long-term. Do you have a bunch of LS friends relocating, too? Are you into any hobbies or sport(s teams) specific to that area of CA? If your explanation is ONLY about the work, they sometimes wonder if that'll be enough to keep you in the area when things like "missing family, and all my friends are back East" arise.
- If you choose ONLY to interview in a CA market, mention that as an indicator of commitment. If they ask you if you're interviewing in other markets, make clear that CA is your first choice. (And if it's not, skip the CA interviews; they're difficult to get if you don't have ties, and you'll make it that much harder for future East Coasters if interviewers get burned by you.)
Good luck. I think we need all the relocated East Coasters we can get out here to help diminish the parochialism of the market. (When I've interviewed East Coast transplants without connections, I've obviously been much more sympathetic to them than many of my native Californian colleagues.)
NB This advice applies mainly to NorCal, as I agree with everyone who said that LA is much easier from the East Coast.