Can you fly straight into Szombathely?
Unfortunately, you can't. But you can fly in Wien, Austria! Szombathely(Hungary) is close to Wien. You can travel with train from Wien to Szombathely, it is 2,5-3,5 hours depends on the catch. Or you can fly to Budapest,then it is 3,5-4,5 hours from there. But in this case you have to travel inside Budapest to the train station, it can be an hour.