It is no problem to take the train to get to Braunau. The train station is just 1 km away from the historic town square. With a public bus it can be reached in a few minutes. The train station on the Bavarian side in Simbach is also within walking distance. Taxis are also usually available at the town square to bring you directly to your destination. Of course you can carry your bike on the trains of ÖBB.
Arriving by bus is another option. The bus will take you directly to the bus station of Braunau at the Kolpingplatz. From this place it is a few hundred meters to the town square. Busus will also take you to the town districts of Laab, Haselbach, Braunau Neustadt or Ranshofen.