While Gov. Andrew M. Cuomo’s troubles dominated the headlines, the bevy of candidates running for New York City mayor trudged onward, dutifully showing up for yet more online forums and occasionally taking swings at their opponents’ foibles.

The city’s new ranked-choice voting scheme is supposed to make the mayoral race nicer, since candidates are vying not only for first place, but also for second, third, fourth and fifth place, too. In such a scenario, it doesn’t pay to alienate a competitor’s supporters.

That friendliness was on display after the Hotel Trades Council, a powerful union, endorsed Eric Adams, the Brooklyn borough president.

Andrew Yang’s co-campaign managers made a point of saying nice things on Twitter. But the bonhomie didn’t last long.

Adams and Yang spar over subways

When Mr. Yang wrote on Twitter that he was “Bronx bound” while on the A train — a line that ends in Upper Manhattan — he gave new life to criticism that he lacked expertise about the city he hopes to govern.

“Someone get Andrew Yang a subway map,” the New York Daily News wrote.

The ribbing didn’t end there. The next day, Mr. Adams, who has placed second behind Mr. Yang in most polls, posted a photo of himself on Twitter suggesting that he knew how to get to the Bronx by subway.

Chris Coffey, Mr. Yang’s co-campaign manager, quickly responded: “Did your car and driver meet you in the Bronx?”

Mr. Coffey pointed out that Mr. Yang had switched from the A train to the D train at 125th Street and traveled to 167th Street in the Bronx to tour small businesses with Vanessa L. Gibson, a councilwoman from the borough who is running for borough president.

It wasn’t the first time last week that Mr. Adams had targeted Mr. Yang for criticism. The two men are also sparring over universal basic income, Mr. Yang’s signature proposal from his run for the Democratic nomination for president.

Mr. Yang introduced a version of the plan for New York City that calls for providing 500,000 of the city’s poorest residents with an average of $2,000 per year, and would cost about $1 billion.

Speaking Friday at a virtual event hosted by the Association for a Better New York, Mr. Adams touted his plan to boost the city’s earned-income tax credit to provide 900,000 New Yorkers with up to $4,000 per year.

Mr. Adams never mentioned Mr. Yang’s name but his language was caustic: He referred to his opponent’s proposal as “UBLie” and “snake oil,” and said the city did not need “empty promises” from “hollow salesmen.”

Mr. Adams’s criticisms are a sign that he’s worried, Mr. Coffey suggested.

“Hitting Andrew Yang, who is widely credited with making cash relief mainstream, at the same time as stimulus is starting to go out defies logic,” he said. “It’s almost as silly as trying to mock a lifetime subway rider when you have had a car and driver for seven years.”

Truth, dare or dance?

The high school students at the Teens Take Charge mayoral forum on Thursday grilled the candidates on tough issues such as summer jobs, funding for the City University of New York and the specialized high school entrance exam. They were ruthless moderators, holding the candidates to the allotted time to answer questions and even cutting them off when necessary.

But that doesn’t mean they didn’t have fun at an event that many participants called the best mayoral forum so far.

During the first “truth, dare or dance” round of the 2021 mayoral election season, the candidates could choose a truth, a dare or a 15-second dance to a song that the students had randomly chosen.

No candidates chose to dance, but as the segment was ending, Shaun Donovan, a former federal housing secretary, was apparently dismayed that he had not gotten a chance to bust a move.

“Can we dance now?” Mr. Donovan asked.

One of the hosts, Carmen Lopez Villamil, offered 15 seconds to allow all the candidates to dance at once.

“For real, we’re going to dance?” Dianne Morales, a nonprofit executive, said with a shocked look.

As the song “Macarena” began to play, Mr. Yang was the first one out of his seat, followed closely by Mr. Donovan and Maya Wiley, the former legal counsel for Mayor Bill de Blasio.

“You’ve got to turn it up a little bit,” said Ms. Wiley.

Ms. Morales swayed to the beat with verve and rhythm. Mr. Donovan did a spin. Mr. Yang looked like he was doing a bit of salsa dancing, while Scott Stringer, the New York City comptroller, stuck to a quick two-step while wiggling a bit. Ms. Wiley also looked like she was grooving, but she was too close to the camera for the audience to check out her moves.

“I love to dance but hoped for the Black Eyed Peas,” Ms. Wiley told The Times. “The Macarena isn’t my flava.”

Unfortunately — or maybe fortunately — no one actually did the Macarena.

Mr. Donovan admitted to not knowing how to do the dance but said he saw the opportunity as the “antidote” to hours of Zoom conferences.

Adams lands the second big union endorsement

Mr. Adams has taken to saying that he will be a “blue-collar mayor.” He talks about how his mother cleaned houses to support their family when he was growing up. Last week, the Hotel Trades Council endorsed Mr. Adams, calling him the “candidate of and for working-class New Yorkers.”

The well-connected union has 31,000 workers, 22,000 of whom are registered to vote in the city. That can mean crucial votes in a crowded field, more small-dollar donations and campaign workers on the ground.

It was the second big union endorsement in the race after Ms. Wiley was recently endorsed by Local 1199 of the Service Employees International Union. It came as the pandemic has shut many city hotels and left workers unemployed. The number of visitors to New York City was down 66 percent in 2020 compared with the year before. Even with vaccination numbers on the rise, NYC & Company projects that tourism may not rebound until 2025.

Mr. Adams recently endorsed a plan with another mayoral candidate, Carlos Menchaca, a councilman from Brooklyn, to turn underutilized hotels outside of Manhattan into affordable housing. Many of those hotels are nonunion.

Mr. Adams is also in favor of a special citywide hotel permit for hotel construction, a policy Mr. de Blasio is trying to push through before his term is out. The Hotel Trades Council is backing the measure.

If the city’s hospitality industry is to rebound, it needs tax relief, public safety, real-time reporting on vaccination rates and a “robust marketing effort,” Mr. Adams said.

A biking mayor?

There is a good chance that the next mayor will be a regular cyclist.

The candidates showed off their cycling bona fides at a forum last week: Raymond J. McGuire showed off a sleek bike perched behind him in his elaborate Zoom setup, and Mr. Adams said he goes for a ride when he is feeling stressed.

Mr. Yang said he got a bike when his first son was born and rode it from Hell’s Kitchen to the Financial District to take him to school.

“It was a game changer for me,” Mr. Yang said.

Many of the candidates said they want to continue to add protected bike lanes. Mr. Stringer plans to double bike ridership, move toward a car-free Manhattan and make sure that bike lanes are clearly separated from traffic so that his sons can ride safely.

“We have to use our children as the barometer for whether we think a bike lane is safe,” he said at the forum.

Mr. Donovan was perhaps the most serious cyclist: He once biked through the South to retrace the 1961 Freedom Rides.

“I’m pretty sure no other candidate in this race has cycled 1,000 miles retracing the route of the Freedom Rides,” he said.

Executive women support Garcia

Let one thing be clear: Kathryn S. Wylde, the executive of the Wall Street-backed Partnership for New York City, is not endorsing Kathryn Garcia for mayor. She said she does not endorse because she will have to work with whoever gets elected.

But she does think that Ms. Garcia, along with a couple of other candidates, would make for a very good mayor. That’s why she co-hosted a fund-raiser for Ms. Garcia, the former Sanitation Department commissioner, last week.

So, too, did another business executive — Alicia Glen, a former deputy mayor in the de Blasio administration and one of the few de Blasio officials to earn plaudits from New York’s business class.

Ms. Garcia said she interpreted Ms. Glen’s support as an endorsement, but deferred to Ms. Glen, who didn’t respond to requests for comment.

Ms. Wylde said that she encouraged Ms. Garcia to run, much as she encouraged Mr. Donovan and Mr. McGuire, because she thinks Ms. Garcia would run the city well. She was particularly impressed by Ms. Garcia’s reform of the notoriously dangerous and inefficient commercial garbage collection system.

“She’s somebody that brings people together to solve problems, and I’d like to see our next mayor be that kind of person,” Ms. Wylde said.

Ms. Wylde has been working in politics since the late 1960s, when there were virtually no women in elected government.

No woman has ever been mayor of New York. Ms. Wylde deflected when asked if she thought a woman could win this time around.

“Historically, in any profession in New York City, women have a tough time getting ahead,” she said.