LLC for out of state rental property, reside in CA
Since your rental property is in Nevada this is where your LLC needs to be registered. If the "business" of that LLC is holding and managing this particular rental property and collecting rental income only then it is safe to assume that this is a purely Nevada business and would not require you to register it in California.
To make sure there is as little connection to California as possible I would also recommend you to open the bank account for this LLC in Nevada as well (technically it is accepted that having a bank account in California does not by itself create "nexus" in California, but I would still stay on the safe side just in case rules change in the future).
As far as income tax goes you pay it all in California, since LLC is a pass-through entity, meaning you will report the income from your LLC on your personal tax return (I presume you file as California resident).
Keep in mind that although you avoid the California franchise tax of $800 a year, Nevada does require you to file Initial List of Members and obtain a State business license (additional $325 in state fees on top of the $75 for regular filing), and the LLC would cost you $125 in Annual Report fee plus State business license renewal fee of $200, $325 total.