I will likely be staying in Budapest so I can combine the GP with a nice city break. Looks like there is options for train or bus, based on what I found at this site: http://www.budapest-life.com/budapest/hungarian-grand-prix
By suburban railway (HEV in Hungarian)
It is relatively easy to reach Hungaroring by public transport. Take the HEV railway from Ors Vezer Square and alight at either Szilasliget or Hungaroring itself, journey time around thirty minutes. The former has a paved walkway to the track, whilst for the latter you will walk over a dusty road.
HEV H8 – http://www.bkv.hu/en/suburban_railway_schedules
Leaves from Ors Vezer tere, end of M2 line.
Ticket holders for the Grand Prix can board a special bus laid on for the purpose. The bus departs from the Pest end of the Arpad Bridge, and takes you to the centre of Mogyorod, the village adjacent to the track.
Train seems the best option, as I assume you can avoid traffic going to the site. But I suppose it could be busy.
Anyone who has been, any suggestions?