Anyone who thinks New Year's Eve is about resolutions, champagne or drunk-driving roadblocks doesn't have kids. For those with children, New Year's Eve is about one thing only -- baby sitters.

All over the Washington area, the search for the essential sitter is underway. Only those with brains, guts, signed contracts complete with nonrefundable deposits or built-in baby-sitting teen-agers have escaped the mad scramble.

"Oh God, you just reminded me. It's terrible. I don't have a sitter yet," Llewellyn Bensfield, the mother of two tots and two teen-agers, said yesterday. "I'm trying to figure out a reason to ground one of the older two kids for New Year's Eve."

Said Justice Department attorney Richard Ugelow: "We don't even go out. It's too frustrating to even look."

Many of those not as resourceful as Bensfield or as pessimistic as Ugelow have turned to baby-sitting services, and anyone who called Sitters Unlimited in Northern Virginia found this to be serious business.

"We sent out contracts to everyone who called us and required 35 percent nonrefundable deposits," said area director Debra Vermillion. "We got about 50 calls and ended up with 15 bookings."

Her service upped its usual $5-an-hour rate for one child to $6 because of New Year's Eve traffic, but no one seemed to balk at the charge for the teachers, all over 21 years old, whom Vermillion said she provides as sitters. "All this week I've been turning people down . . . . But people do cancel at the last minute, and we might have something open on Monday."

Another popular way to handle the perennial problem is to send the kids off to an all-night New Year's Eve party of their own. The Greenbelt Recreation Department, for instance, is offering a "structured recreation program" for children 6 to 12 years old, with games, movies, party snacks and a light breakfast. All each child needs is a reservation by 5 p.m. Monday; a sleeping bag, pillow and pajamas, and the $20 fee to get in $10 for the second child in a family , according to the program's sponsor.

On Capitol Hill, Supertots, which runs nursery and day care programs, has a toddlers' blast with cupcakes, punch, hats and noisemakers.

"We set the clocks ahead three hours and celebrate at 9 p.m.," said owner Lenore Riegel. "The kids love it."

Part of the problem, said Fetneh Fleischmann, who lives in the Barnaby Woods section of Northwest D.C., is that the traditional teen-aged baby sitter seems to be in short supply.

"The kids of baby-sitting age are very socially active, and I have the feeling most don't need the money," she said. Fleischmann and baby Shirin are still hunting that elusive sitter.

Others, however, have solved the dilemma by throwing and going to parties where the children are welcome. Anne and Gus Edwards attend a sit-down dinner in their Old Town Alexandria neighborhood where dark-haired Scottish bagpipers drop in after midnight for a traditional ceremony called "First Footing," according to Anne Edwards.

"The Scottish believe that if the first person over the threshold on New Year's is a dark-haired stranger, you will have good luck the rest of the year," she said. "We wake the children for it, and it's a lovely tradition."

Carolyn Bonker, the wife of Rep. Don Bonker (D-Wash.), learned the hard way that you have to plan early. This year she moved up the date of arrival from Jan. 1 to Dec. 30 for a teen-ager coming to live with them, so she would have a built-in baby sitter.

"We've gotten in hot water previous years," Carolyn Bonker recalled. "One time, my husband, bless his heart, insisted that I go out, and he stayed home as the sitter."