When Carolyn and Bill Thornton decided to retire to Manhattan from San Antonio, where Mr. Thornton had been mayor in the mid-1990s, they started by looking at apartments in placid residential neighborhoods like the Upper West Side.

But they always came away from the tree-lined streets feeling something was lacking. They were moving to New York, in part, to be closer to their son and daughter. But they weren’t coming here for the peace and quiet. What they wanted was action.

They found it on the 34th floor of a Herald Square high-rise.

“When I walked in here, I was like, ‘Oh, my gosh,’” Ms. Thornton said. “We wanted those views.”

Mr. Thornton added: “It’s a great way to wake up — seeing the sky, the clouds, the light. At night, it’s so beautiful. We always say it looks like diamonds.”