Just before noon on Thursday, James Browar pushed out of a Starbucks on Eighth Avenue near Times Square, laden with news that was simultaneously getting worse and more urgent by the minute.

“No bathroom,” announced Mr. Browar, 20, who came from New Jersey for the St. Patrick’s Day Parade.

“What?” asked Lydia Piazza, who also made the trip.

“I asked if it was for paying customers,” Mr. Browar said. “They said there’s no bathroom whatsoever.”

He told a stranger, “I must have walked three-quarters of a mile.”

That doesn’t seem very far. New York City, after all, is one of the most public-bathroom-resistant places in the world, and few days in the year would make even the most hospitable restaurant less likely to throw open its restrooms than St. Patrick’s. But forget that. The natives have mapped out the facilities, like rock climbers knowing where to drive their anchors. There were, however, nearly 57 million tourists throughout 2014, many of them not used to our ways.