Unfortunately, Dornbirn does not have an international airport, the nearest airport is Munich or Zurich. I would recommend Munich Airport and from there take a rental car to Dornbirn or take the train. The rental cars in Munich are definitely cheaper than in Zurich.
If you arrive by train, that’s no problem either, it’s a short walk from Dornbirn train station to the hotels in Dornbirn.
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