Budapest Nyugati Railway Station is one of the three main railway stations in the city, in this case serving the north of the city. It was opened on October 28, 1877. It has become one of the most important stations in the city and is served by various bus lines, tram lines, and metro lines. It's one of the main railway station for tourists arriving from neighboring European countries as well as a main point of departure for tourists heading to the international airport. If you're planning on taking the train to the airport, the journey takes around 25 minuted.
Budapest Keleti Railway Station (commonly known as Keleti or Keleti Palvaudvar) is one of the three main train stations serving the city of Budapest. It was opened on August 15, 1884 and currently serves the eastern part of the city. If you go into the lobby of the station, you can actually see some beautiful frescoes painted by Károly Lotz and Mór Than as well as a monumental entryway designed by Gyula Rochlitz.