The tram line No 2 offers the best view from a city transportation vehicle. It goes all along the Danubeside from Jaszai Mari ter (reachable with the tram 4 and 6 for example) passing the Parliament, the Hungarian Scientific Academy, the Chain Bridge, the Danube Corso, the Castle and the Gellert Hill with the Citadel. Don’t forget to get off at the Fovam ter, because there is nothing really special to see after that. But overe there you will see the building of the Economical University and the Old Market Hall.
Website: http://www.bkv.hu/english/villamos/2_jaszai.html