After her husband died a year ago, Alice Williams, 77, gave up the couple's Fairfax City apartment and moved to Reston, the meticulously planned "new town" in the Northern Virginia suburbs.

"The social worker said Reston was ideal" for elderly people in search of peace and quiet, said Mrs. Williams.

Today, Mrs. Williams and her fellow residents at the Hunters Woods Fellowship House for the elderly in Reston are feeling less than idealistic. They seldom leave their apartment at night and they say they are afraid to go out alone even in the daylight.

The reason: a wave of assaults and robberies -- attributed mostly to idle youngsters -- that Reston residents thought they had left the city.

Mrs. Williams was injured recently as she shopped at the nearby Hunters Woods Mall, where police say much of the trouble is focused. She was attacked by a "little squirt" who blackened her eye, threw her to the ground and tried -- unsuccessfully -- to steal her purse.

Fairfax County police records for 1978 show 37 robberies and 159 assaults were reported in Reston, a community of 37,000 -- 27 and 21 percent higher, respectively, than the rate for such crimes in the sprawling county as a whole.

And while residents, merchants, politicians, and police disagree on whether the assailants are prediminantly well-off or poor, all sides say the offenders are young.

Several shopowners and elderly residents said the offenses are committed by youngsters between the ages of 8 and 11.

"It's unbelievable how young they are," said Fairfax officer L.R. Custidero, who walks a foot patrol between 2 and 10 p.m. at Hunters Woods and Lake Anne Plaza, another Reston shopping center.

"There are drug deals going down, purse snatchings. The problem is similar at Lake Anne. The lake (the geographical centerpiece of Reston) attracts them. I guess it's pretty romantic."

The effect on Reston shopowners has been direct and their litany of complaints ranges from nuisances and harrassments by youngsters to claims of lost business.

"We're dealing with very serious fear problems there," says Fairfax Board of Supervisors Chairman John F. Herrity. "I've had people come up to me and say that you need a gun to shop there."

"You're always watching out for shoplifters," said Linda Ward of Sam's Tailoring Co. in a recent interview. The shop had no customers that afternoon as Ward groused about "hordes of kids who should be in school, but hang around here."

"Everybody gets their share of the problems," said Ken Mawyer, assistant manager of a Drug Fair. "The kids are scaring the elderly with bikes and skateboards. And there is a massive amount of shoplifting. They come out here to create hell."

Mawyer said the youths "have bothered business" at the shopping mall, and Sharon Stratton, a sales person for the Heel and Toe shoe store, agreed.

Stratton sais she hadn't had a customer in the last 90 minutes as she talked about "exasperating juveniles.

"You get teen-agers loitering around, a lot of vandalism from little kids. The merchants have to endure a lot of nonsense." she said. She recalled the time a youth threw a chuck of wood at the stores' entrance before he entered the shop to call her a "witch."

"Then he came right inside, like he hadn't done anything. I threw him out, the nervy little . . . Stratton said.

Flood Thomas, an assistant manager of the Baskin-Robbins ice cream emporium on the mall's main causeway, believes the juveniles seek out his store most often.

"They cause a bunch of problems. I've given some kids part-time jobs here who come back saying their parents don't want them to work here. They think it's too dangerous."

"The kids are street wise," added Mawyer. "The mall is built for walking and the police don't get here quickly enough. The kids have disappeared before they arrive."

Mawyer and several other retailers and residents blame Reston's problems on low-income renters. They singled out Stonegate, a racially and economically mixed, subsidized housing project near Hunters Woods Mall, as the main source of trouble.

"A lot of the kids" are from Stonegate, said Mawyer, "They come in and dare you to ask them to leave."

While some politicians, including Herrity, share the view that low-income housing in Reston is linked to the community's crime wave, others disagree.

The pilfering at Hunters Woods is "done by well-educated, well-off kids," said Supervisor Martha Pennino (D-Centreville), who accused Reston merchants of looking for a scapegoat for chronic business ills.

"The rents on the shops are so high that many businesses over the years have gone under. The way the mall is designed is simply not conducive to good business. People go to the liquor store and the Safeway, and then leave," Pennino said.

Several officials interviewed agreed that stepped-up foot patrols in the area would help deter crime -- a statement welcomed by Fairfax Lt. Roy Irvin, assistant commander of the Reston substation, Irvin hopes to add 18 officers to the area's current force of 36.

Irvin, who has been a police officer in the county for 19 years, said it is unfair to blame subsidized housing for the area's crime.

"We arrested ambassadors, and a presidential cabinet member of a former administration for shoplifting in the county. You can't lay the blame totally on low-income people," Irwin said.

Irvin added that Stonegate "has been drastically improved" since Nathaniel Poon, Stonegate's resident manager, and Carolyn Payne, social services coordinator for the Stonegate facility, took over the complex last May.

Poon, who lives on the premises and patrols the property himself three times a night, said area residents are using his project as a "scapegoat."

"I would suggest that those people get with it," Poon said. "There are bad kids in $200,000 homes, too. It takes more than a blueprint to make an ideal community. They have to be willing to communicate with us, and they aren't right now."

Ben Weimer, executive director of the Reston Community Center at Hunters Woods, also blamed the attitudes of Reston residents as part of the problem.

"It's always been convenient to blame the poor people," Weimer said. "The attitudes toward the youth of the community has a lot to do with it. You have to be open and willing to deal with people.

"We've got the plan for the 'ideal' community here," Weimer said. "It's a shame we aren't ready for it."