A task force created by New York City Mayor Bill de Blasio and police is attempting to answer those questions.
Over the past few years, New York's famed Times Square has been virtually overrun with costumed characters such as Elmo and Spider-Man, and, more recently, topless women wearing only brightly-colored body paint and tiny underwear. Some sport American flag patterns and other designs on their bodies.
But the friendly faces of the characters can be deceiving. Each day, the New York Police Department receives a number of complaints about alleged harassment and other acts that frighten and upset both visitors to and residents of New York.
"This task force will identify the best legal and regulatory ways to move forward and keep Times Square the popular destination site for visitors and families from New York City and across the world," Mayor Bill de Blasio said last week in a press release announcing the new initiative.
The task force will include representation from a number of city offices, including the NYPD, the Department of City Planning, the Department of Transportation and the Department of Consumer Affairs. It will be chaired by Police Commissioner Bill Bratton and City Planning Commissioner Carl Weisbrod.
Complaints of aggressive solicitation
There have been dozens of incidents over the past few years involving these characters. The violation usually involves harassment or aggressive solicitation for tips after tourists take photographs with the entertainers.
Just a few weeks ago, a video emerged on YouTube that showed a man dressed as Spider-Man punching and wrestling with a pedestrian outside of the Times Square Toys R Us. And last week, police said officers confiscated two large snakes they say a 34-year-old man was trying to put on passers-by's necks.
Those are only the most recent in a string of headline-grabbing incidents in the famed New York plaza over the past few years.
In 2013, a man dressed as Cookie Monster was accused of shoving a 2-year-old after the child's parents declined to pay him the requested $2 fee after taking a photo. Last year, a man who dressed as Woody from "Toy Story" was charged with three counts of forcible touching and three counts of third-degree sex abuse.
CNN was unable to verify the status of their cases.
City officials worry that such incidents could deter tourists from visiting Times Square, which is often called "the crossroads of the world." Many of the incidents involve the street performers chasing or harassing visitors for tips after taking photos.
Up until this point, it has been difficult for city authorities to enforce rules for Times Square's problematic entertainers.
First Amendment rights protect the performers' decision to wear whatever they wish in public. Additionally, a ruling in the New York State courts in the early 1990s permits women to be topless in public, just as men can.
But that is not stopping the city government from pursuing new regulation.
"As a progressive who believes in civil liberties and believes in our First Amendment, I understand the legal challenge here, but I don't think that's the end of the discussion," de Blasio said. "We are going to look for every appropriate way to regulate all activity that involves either begging or asking people for a contribution based on the opportunity to take a picture, for example."
'All of a sudden, it's an issue'
Some of the performers are sticking to their guns. A topless performer who identified herself as Angel told CNN affiliate WPIX that she finds the new debate "ridiculous."
"It's been legal for a woman to be topless anywhere a man can be topless in New York State since 1992," she said. "So now, all of a sudden, it's an issue."
One proposed solution, mentioned by both de Blasio and Bratton, is to rip out the Times Square pedestrian plaza. That plaza, which was completed in late 2013, is where many tourists -- and, consequently, the performers in question -- gather.
"I'd prefer to just dig the whole damn thing up and put it back the way it was, where Broadway is Broadway and not a dead-end street," Bratton told 1010 WINS, a local New York City radio station.
"The activity is not occurring anywhere else in the area," he continued.
It is still unclear exactly what action the task force will take against the caped crusaders, furry characters and painted women, despite the varying challenges at hand.
"I'm not satisfied that we've used every tool in our arsenal yet," de Blasio said. "And I don't like the situation in Times Square. We're going to address it in a very aggressive manner."