How does Woodward find Mrs. Mitchell?

Woodward knew the couple had moved into the Essex House, so he stopped by and called until he was able to get their room number.

The Mitchells had moved back to New York and were living at the Essex House on Central Park South. Woodward took the last night flight to New York on September 21, hoping to catch Mrs. Mitchell at home the next morning, after her husband had left for the offices of Mudge, Rose, Guthrie and Alexander, the law firm in which he and Richard Nixon had both been partners.
At nine the next morning, Woodward asked the clerk for the room number of J. N. Mitchell. No one was registered under that name. He went to a telephone booth down the street and called the Essex House. “Give me the room where the Mitchells are staying at once, hurry,” he said.
“Room 710,” the switchboard operator said, ringing the extension.