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