National Parks follow state law. That means UOC* unless you have a CCW. California state parks and beaches are no-carry without a CCW. Municipal parks are preempted from enacting carry bans but many of them do anyway.
*NPS rangers are currently interpreting California law to mean that loaded carry is prohibited anywhere a shooting ban is in effect. Since every National Park in California has a federally-issued shooting ban, they are enforcing UOC. However California case law suggests that only county-issued bans may trigger PC 12031, and absent the county prohibiting shooting there, it should be legal to LOC in most National Parks. However this is not recommended unless one wishes to possibly become a defendant in a criminal case at their own expense. Don't carry loaded in a National Park without a CCW until a more clear ruling on the law becomes available.