Both destinations are served by Port Blair (IXZ). Since there's no flight route between them, the best way to travel is by road.
Andaman Nicobar
Fly to Port Blair (IXZ), then travel by road to Andaman Nicobar. Taxis, buses, and private cabs are available from the airport.
Port Blair
Fly to Port Blair (IXZ), then travel by road to Port Blair. Local transport options include taxis, auto-rickshaws, and state buses.