There were moments for instruction, too, as when Innes suddenly made a sharp right — toward the open door of a perfume store. The dogs would soon get used to such distractions, Ms. DeMarco said. For now, Ms. Faul pulled him back on course.

As visual as Times Square is, with its billboards and swarm of activity, Ms. Faul said that its aural energy was also impressive.

“I feel like I’m in a carnival city,” she said. “All the noise, all the beeps, all the people, the different languages you hear. The noise echoes off the buildings. It’s like being at Mardi Gras. Crowds of people everywhere.”

They walked by the TKTS booth selling theater tickets and headed past Broadway theaters. Ms. Gee praised the way Ozma ignored the blaring sirens and kept her away from creeping tour buses and rumbling dump trucks.

“She seems to focus even better in the chaos,” she said, adding that there was only one problem.

“She’s going to be disappointed when we go home.”