I feel like raptors were under-represented at Omaha, adding Harris' Hawk here would help fix that problem, and to me they are an iconic "american southwest" species. The Burrowing Owls could be moved into one of the wall exhibits, such as the one that contained only quail.
According to ISIS, they have Harris's hawk, red-tailed hawk, rough-legged hawk, Swainson's hawk, golden eagle, and bald eagle, but I guess that most of these are at their other facility.
In the past they had both American kestrel and turkey vulture in the Desert Dome.
When I was there I went in the bird holding spaces throughtout the zoo and the only birds of prey I remember seeing were 1 Spectacled Owl and 1 hawk, I think it may have been a Harris'.
Interesting, I do recal spectacled owls in the Lied Jungle, but that was years ago. They also used to have eastern screech owls in the swamp area of Kingdoms of the Night.