Hi 304 HighDrone,
I think there is some confusion as to Airports A and B. That classification is DJI and has nothing to do with the FAA.
The FAA classifies them as Class B, C, D and E. The airports that DJI calls A and B are pretty much those in FAA Classes B, C and D. These are airports that have operating control towers.
You need to find out if the airport you are Intersted in is in any of these 3 classes. Airports in Class E are small airports without control tower. Use this link
https://www.airnav.com/airports/ to find the contact and phone information for any airport in the U.S. Also use Google Earth to find the correct name of the airport.
If the airport has a control tower, it may be difficult to get them to go along with you but you can try. If the airport does not have a control tower, then the owner/manager of the airport should be able to help you.
Things that you want to consider when you are informing them:
Try to stay away from the approach ends of the runway.
Inform them that you will be flying below 400ft or lower if possible.
Stay away from any manned aircraft.
Where and when you will be flying.
The proper FAA office to contact (FSDO), is the one having jurisdiction over the area you will be flying. Use this link to find this information:
http://www.faa.gov/about/office_org/field_offices/fsdo/
I hope this helps!