Caves of Steel indeed (I seem to recall a more elaborate section but can't find it again):

There was the usual, entirely normal crowd on the expressway: the standees on the lower level and those with seat privileges above. A continuous trickle of humanity filtered on the expressway, across the decelerating strips to localways or into the stationaries that led under arches or over bridges into the endless mazes of the City Sections. Another trickle, just as continuous, worked inward from the other side, across the accelerating strips and onto the expressway.

There were the infinite lights: the luminous walls and ceilings that seemed to drip cool, even phosphorescence; the flashing advertisements screaming for attention; the harsh, steady gleam of the “lightworms” that directed THIS WAY TO JERSEY SECTIONS, FOLLOW ARROWS TO EAST RIVER SHUTTLE, UPPER LEVEL FOR ALL WAYS TO LONG ISLAND SECTIONS.

Most of all there was the noise that was inseparable from life: the sound of millions talking, laughing, coughing, calling, humming, breathing.

No directions anywhere to Spacetown, thought Baley.

He stepped from strip to strip with the ease of a lifetime’s practice. Children learned to “hop the strips” as soon as they learned to walk. Baley scarcely felt the jerk of acceleration as his velocity increased with each step. He was not even aware that he leaned forward against the force. In thirty seconds he had reached the final sixty-mile-an-hour strip and could step aboard the railed and glassed-in moving platform that was the expressway.

No directions to Spacetown, he thought.

Vance also had a novel with mechanical roads. I guess that was a common trope back when the first mechanical stairs appeared.