I think that not many zoos have exhibits equipped for marine birds probably. They are my wife's favorite bird species, so we are always on the look out for them at zoos or aquariums. I've seen the ones at Omaha that you mentioned. These are the other places that I've seen them:
The Monterey Bay Aquarium has tufted puffins in a decently size aquarium tank. They also have common murres (non-releasable rehabbed birds I think; there are wild common murres that you can see from the aquarium deck sometimes).
The Aquarium of the Pacific in Long Beach also horned puffins and rhinoceros auklets in an okay indoor aquarium.
The Bronx Zoo has tufted puffins in an exhibit in their aquatic bird house. The Central Park Zoo also has tufted puffins.
The Point Defiance Zoo in Tacoma, Washington has tufted puffins in a nice large outdoor aviary.
The Oregon Aquarium has tufted puffins in an in a large outdoor aviary.
Sea World San Diego has tufted puffins in a nice large exhibit in the penguin area:
Puffin Exhibit in SeaWorld San Diego - YouTube
I think that the Cincinnati Zoo has puffins and alcids also?