On the Andrássy út.

Vaguely put, the previous ruler wanted Budapest to have a straight road that cut through the city just like that in Paris. And hence, Budapest has a straight road that is a must see - Andrássy út. 

the heroes monument stands tall at the end of Andrassy ut.

This Avenue is an elegant 2.5 km (2 mi) long tree-lined street that covers the distance from Deák Ferenc tér to the Heroes Square.

The fact that most of the buildings at the side of this road is very well preserved and hence put this road as well as part the underground structures, with Castle of Buda and the bridge (if I'm not mistaken), as one of the heritages in the UNESCO list for its defined architecture and township planning is also why one should not miss walking down the road. 

Although, technically, I probably only walked for about 500m or so, and I took the chance boarding the public transport instead. LOL