Szombathely sits in the far west of Hungary, close to both the Austrian and Slovenian borders.
By train, there are direct services from Budapest (Keleti or Déli station, roughly 2h45–3h30) and from Vienna (around 1h30 to 2h via Bratislava-Petržalka or Wiener Neustadt, with one change). Local trains run to Sopron, Szentgotthárd, and across the border to Graz.
By car, the M1 motorway gets you most of the way from Budapest before you peel off at Veszprém or Sárvár; allow about 2h30. There is no commercial airport; the nearest are Vienna (about 1h45 by car) and Budapest.
There is also a small regional airfield used for general aviation.