The county I'd like to put a private runway (for my use only) in doesn't require any special permits because the property is zoned Agricultural, BUT they do require some form of acknowledgement from the FAA that the FAA doesn't have a problem with it being in that location. How do I go about getting something like that from the FAA? Who do I contact?
You're probably already aware that the FAA itself does not require the operator of a private airfield to receive any kind of approval from the FAA. However, there is a process in place to register a private airfield, and indeed the notice (not approval) is mandatory. The result of that process might satisfy your local authority.