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