by a car

From Vienna Center, it is approx..300km, and takes 3.5 hours

by train and taxi

Take a train from Vienna to Klagenfurt.
It takes approx..4 hours.
Take a taxi at Klagenfurt Train Station.
It is about 16km, and takes 20 min.

by plane

There is a direct flight from Vienna to Klagenfurt which takes 45min.
Take a taxi at Klagenfurt airport.
It is about 12km and takes 12 min.