Both destinations are served by Rajiv Gandhi International Airport (HYD). Since there's no flight route between them, the best way to travel is by road.
Hyderabad
Fly to Rajiv Gandhi International Airport (HYD), then travel by road to Hyderabad. Taxis, buses, and private cabs are available from the airport.
Nalgonda
Fly to Hyderabad (HYD), then travel by road to Nalgonda. Local transport options include taxis, auto-rickshaws, and state buses.