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