Looks like this thread has been inactive for a while - but I might have some useful info as it pertains to Hermosa Beach:
The city does indeed require a permit, but in my experience it was pretty painless to get (other than the cost). I am not sure how useful this permit is however - as I was told by a Lifeguard today on Hermosa Beach (after showing him my permit) that drones are prohibited on all LA County operated beaches and Hermosa Beach City does not have the authority to issue these permits in the first place. (This is the first time I've ever had an issue after several flights - in fact one lifeguard told me it was no issue prior to this occurrence).
For questions regarding size - the permit looks like a US postage stamp and has a unique number. It's not large at all.
I wrote an email to the LA County Lifeguard asking them to point me in the direction of this ordinance that prohibits flights on county beaches. I'll let you all know if I ever hear back.
It seems that we are running out of places to fly in LA.
Perhaps this is what he was referring to:
LA County Municipal Code:
17.12.425 - Model operation prohibited.
No person shall operate any model airplane, boat, helicopter, or similar craft in, on, or over any beach or the Pacific Ocean except in an area that may be established and/or designated for such use by the Director, and subject to all rules and regulations pertaining to such area.