Not far from the dock, stop at Ötkert (Zrínyi u. 4/A) and have a #2 Långos (cheese & sour cream). My Hungarian pal took me there, said it was the best and most authentic he'd found, he's lived there nearly his whole life. Have a beer or coffee, too. Then, St Stephan's Basilica is just up the street, past the bronze cop.
Then, go about 3 blocks north to the Citizen's Holocaust Memorial. Continue across the street to Liberty Square.