Ljubljana Jože Pučnik Airport: The good option is a pre-booked shared shuttle or rental car, not trying to stitch together airport and regional buses. By car it is roughly 1 hour via the A2 and Jesenice; a shared shuttle is commonly the sensible car-free choice, but book it in advance and expect the fare to vary with demand. Public transport is possible only with connections and is slow for a short distance.
Ljubljana bus and rail station: Use a direct regional bus to Kranjska Gora when the timetable offers one; allow about 2–2½ hours and roughly €10–15. This is better than taking the train and assuming it reaches the resort: Slovenia’s rail line terminates at Jesenice.
Jesenice railway station: This is the nearest railhead. Connect to Kranjska Gora by regional bus; allow roughly 35–45 minutes and a few euros. It is the practical rail approach from Ljubljana or Austria, but check the bus timetable before committing to a train arrival—services are not metro-frequent.
Klagenfurt Airport: A rental car is the genuinely useful transfer: roughly 1–1¼ hours, depending on the border route and conditions. Public transport involves multiple changes through Austria/Jesenice and is rarely worth the time for a short stay.