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