The first thing we did when we hit Budapest was to go get our train tickets for the trip to Prague. That's not a slap at Budapest, by any means... long train journeys in Europe almost always require seat reservations. That's something you don't want to be without on a trip that takes 6½ hours (standing that long would get real old real fast) so it pays to reserve as early as possible.
The weather in Budapest that day (27 June) was unspeakable... it hit 37°C (body temperature) and only the trains and buses are air-conditioned.
'palyaudvar', by the way, is the Hungarian word for 'train station'; 'gare' in French; 'Hauptbahnhof' in German.