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