Could it be "The Western Wizard"? Just going by the name, because you thought Westward was in it - but it is about wizards, and there are Falcons. It's part of the Renshai fantasy series.

Could it be The Western Wizard (1992) by Mickey Zucker Reichert?

The second novel in a brilliantly conceived epic by the author of The Bifrost Guardians. Colbey, the Renshai of prophecies, must struggle to integrate the gift/burden given him by the Western Wizard and train the first new generation of Renshai warriors. Sequel to The Last of the Renshai.

Just going by the name, because you thought 'Westward' was in it - but it is about wizards, and there are falcons. It's part of the Renshai Trilogy.