New York City sent 18 of Radio City's famous Rockettes tapping and kicking their way through Washington yesterday in an effort to lure convention business to the Big Apple.

The Rockettes ended a week-long "sales blitz" by the New York Convention and Visitors Bureau with "The Big Apple Show." The elaborate extravaganza, staged for meeting coordinators from some of the 2,600 trade associations and professional groups based here, was part of New York's attempt to increase its bite of the $15-billion-a-year convention business.

Guests dined on crabmeat cocktails and beef tenderloin as they watched the chorus line tap out the Visitors Bureau's promotional campaign, designed in part to lure business for New York's new convention center, set to open in 1984.

According to Charles Gillett, president of the bureau, the tourist and convention business is New York's second largest industry, netting over $2.1 billion in 1981--a drop from the preceding year. According to Gillett the show was part of New York's effort to re-stimulate its tourist industry. "There has been a slight decline in the convention and tourist industry across the country and although we haven't had as great a decline, we feel we need to get out and keep on pushing the city."

"We don't want to be taken for granted," said Gillett, who also noted that New York intended to dispel its big, bad city image. Gillett's group will take the show to Chicago (sans Rockettes) in April and, of all places, to New York.

Professional singers sang, "Urban crises, how I love them" as the Rockettes waited in the wings for one of their four appearances.

The bureau's "push" included six salesmen who descended on Washington on Monday to make personal contact and calls on the city's numerous conference coordinators. The Washington metropolitan area is home to the greatest number of association headquarters and as such represents a lucrative market for conference-hungry hotels and convention centers.

While Chicago ranks as the nation's number one convention host, the New York promotional team spared no cost in their attempt to take-over the coveted spot.

Robert S. Weatherston, director of catering for the Capitol Hilton, estimates the bill for the luncheon and preceding reception alone will range between $60 and $70 per person. Weatherston, a veteran of city self-sell campaigns, noted that, "In the last year we've had Chicago for a breakfast, Dallas and its cheerleaders for a reception, and Las Vegas and a comedy team for lunch."

"Vegas, with its big-name entertainment" said Weatherston, who makes note of the popularity of the various city shows, "is always a sell-out."