Generally, parades go from Battery Park north to City Hall (where there's speeches and keys to the city given). This runs through the financial district, so in the past ticker-tape was plentiful, and was released from buildings to celebrate the heroes. Nowadays, tickertape has been replaced by shredded paper and confetti.

As for the name "Canyon Of Heroes", Broadway has many skyscrapers and walking beneath them and looking up does give the impression of being inside a canyon.