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