NEW YORK -- Anyone who knows this city will tell you that this is the time to visit. The first cool gusts of autumn have pushed summer aside, children are back in school and the U.S. Open has returned to Flushing Meadow.

It was the tennis that brought Brian Watkins here. On Sunday, the dusty-haired 22-year-old visitor from Utah attended the matches in Queens with his parents and brother. Then they rode the subway to the station at 53rd Street and Seventh Avenue, where he was stabbed to death with a four-inch knife.

Random assaults have become almost boring to many New Yorkers in a city known for the vagaries of its violence. Fourteen children, several of them infants, were shot by accident this summer. To many people, that seemed to symbolize a city that has lost its grip. Police officers are wounded so often that a permanent telephone line, C-O-P S-H-O-T, has been established in case witnesses want to call.

Watkins was the 18th person slain in the subways this year, or the 17th if you agree with the transit police that one man beaten to death was killed in self-defense.

But even here, some crimes stretch the bounds of belief. The brutal rape of the Central Park jogger was among them. The death of Brian Watkins is another, partly because the tale of the naive traveler in the wicked world of the big city has a certain appeal for many New Yorkers. It makes them feel worldly and cosmopolitan. It makes them feel as if this horror could not really happen to them.

But even the most blase' of New York's aloof citizens have stopped thinking that way. The death struck a fundamental chord. Watkins was killed while attempting to protect his mother, Karen, from the attack by eight young gang members who police said were looking for money to go dancing. It happened on a subway platform in midtown Manhattan, a clean station that is just a block from some of the city's largest hotels and has little history of violent crime.

"I can't pretend it isn't horrifying," said William J. Bratton, chief of the transit police whose primary duty of patrolling the subways makes it nation's the fifth largest police force. "A crime like this is like a plane crash. No matter what the odds are, there is a sense it could happen to anyone at any time."

Bratton makes a point of noting that, even now, the odds of becoming a victim on New York's subways are low. Of 2,000 homicides here last year, only 20 occurred in the subways. In the course of a day, perhaps 25 people are robbed on a system that has an average daily ridership of 3.5 million, while hundreds are similarly victimized on city streets.

The Watkins case gained notoriety because the victim was a tourist trying to save his mother from the ravages of New York street toughs. City politicians have competed with each other to offer condolences to dazed family members, who testified yesterday before a grand jury before heading home to Provo to arrange a funeral.

But for the millions who must use the subway to get to work, this event is another reminder of a war waged daily against crime in their homes, on their streets and in their subways. For many of them, there is no escape, no costly taxi rides, no chance of moving to another place.

"I can't tell you how bad I feel for that family," said Kevin Wilenson, who shines shoes a block away from the station where Watkins died. "But this city is sick, man. Every day, something like that happens, and nobody knows about it. Every day."

He shrugged and turned away, because there is little else he can do. The slaying, and those that preceded and will follow it, certainly will intensify cries for more police and harsher penalties for criminals. But as long as the type of knife used to kill Watkins is sold in half of the variety stores in Times Square, it will be difficult to recruit enough police to erase this crime wave.

Ever since the slaying, tourists have trekked to the subway station, apparently looking for something on the platform where Watkins died.

"That could have been me," said Yvonne Wilmer, here with her

family from North Carolina, before boarding the E train to Queens. "That could have been anybody."