Budapest has been more left leaning for a long time. The 2010 elections were special because people everywhere were very fed up with the previous socialist government for various reasons: Corruption, some effects of the global crisis were blamed on them (but they definitely contributed their own share of mismanagement), and of course the "Őszöd speech" leak wherein the PM admitted at a party meeting that they've been lying for years about the economy and they haven't got anything of significance done over the years prior.
The point is, before this landslide victory of Orbán in 2010, Budapest used to be a socialist and left liberal bastion, along with a few other cities such as Szeged. Budapest's mayor was the same left winger (Demszky) for the 20 years between 1990 and 2010.
The divide between cities and the countryside is huge though. Orbán is still overwhelmingly popular among villagers and the poor.