The very first American soil that Prince Charles and Princess Diana step on will be Hawaii's Thursday night. Hawaiians, of course, think that's only fitting since another Britisher, Captain Cook, "discovered" the place.

Nobody's suggesting that what happened to Cook will happen to the royals -- he overstayed his welcome and never got out alive. After an airport greeting by Hawaii's governor, the couple will rest up at the posh Kahala Hilton, where a handwritten note from First Lady Nancy Reagan awaits them. Mrs. Reagan is also sending flowers.

And, you guessed it, a jar of jellybeans. Meanwhile, in Palm Beach, Prince Charles' pal, millionaire industrialist Armand Hammer, has been getting a bit of a cold shoulder.

It wasn't enough that Pat Kluge, wife of Metromedia's billionaire chairman John Kluge and cochair of the Nov. 12 ball benefiting Hammer's United World College, had been exposed by the British press as a former nude model for Knave, a British skin magazine.

Nor was it enough that the Palm Beach town council seemed determined to ban the ball because the $10,000-a-couple proceeds were benefiting an out-of-town charity. College backers eventually solved that problem by donating $75,000 to local charities.

Taking a little more getting used to in some Palm Beach circles are Armand Hammer's Russian connections. Town council member Nancy Douthit called the school "a training ground for the KGB."

"There are lots of people who wonder how he gets along so well with the Russians," John Bryson, who's published a book on traveling with Hammer, recently told The Miami Herald. "The right wing really gets jumpy. His father founded the American Communist Party, too. And, you know, I get the feeling he's spent his whole life trying to overcome that. He tells everyone -- the Russians especially -- that he's the biggest capitalist around."

Last week, Pat Kluge solved part of Hammer's problem by deciding to go abroad the night of the party -- even if Charles and Diana, whom she claimed to have met "four or five times," are coming. They're flying to Palm Beach that morning with Hammer aboard his private jet.

After the news of her "Knave" history, Kluge had said she didn't think Hammer knew about her past "although my husband and all our friends do."

When he did find out a month ago Hammer reportedly rushed to the rescue, calling the 3rd Viscount Rothermere, publisher of The Daily Mail, to ask that the Kluge story be killed. Rothermere listened and subsequently summoned the reporter, who came armed with copies of the now-defunct Knave magazine showing the former Patricia Rose in full-frontal nude pictures.

The story ran. Juggling life as a senator's wife may be a lot different than juggling it as a governor's wife, and when it's a Rockefeller who's also on the board of the Corporation for Public Broadcasting, the juggling act becomes an adventure story with audience potential.

So it is that Sharon Rockefeller speaks to alumnae of National Cathedral School for Girls tomorrow night at The Washington Club. Though not an NCS alumna herself, she's both board member and parent (daughter, Valerie, 14, is a ninth grader). Rockefeller, wife of Sen. Jay Rockefeller (D-W.Va.), continues to steadfastly oppose Reagan administration efforts to reduce federal support of public television. Her term expires in 1987. Who better to write "Women at War" than one who has spent years warring with America's presidents? Veteran reporter Sarah McClendon has just signed a contract with Harry N. Abrams Inc. for what literary agent Audrey Adler Wolf describes as a "healthy five-figure" sum. McClendon, 75, had begun updating an earlier book, "My Eight Presidents," when Abrams' editor in chief Paul Gottlieb asked her to put it aside and do one on women in the military. McClendon, a former WAC, could hardly refuse. It's already a given that no self-respecting embassy trying to get ahead in this town dare be without its lobbyists. Now comes the ultimate in embassy handouts: video press releases.

Austria has taken that concept to new heights. In the first of a two-step campaign designed to purge all those cliche'd notions about its waltzes, pastries, Lippizaner horses and boys choirs, Austria bought time on American Cable Television (sometimes called "The Learning Channel") to air a six-part documentary titled "Austria: The Festive Europe." The series has been running weekly since mid-October.

The second step is making the series available by satellite, without charge, to 1,300 commercial TV stations around the United States. What sets the Austrian series apart from similar efforts by other countries is that Don North, who heads the Washington-based Northstar Productions, was hired to translate the country's assets into the American vernacular by portraying its contributions in high technology and environmental protection as well as in culture, tourism and gourmandizing.

Austrian press counselor Walter Greinert says Americans have a very "favorable" impression of Austria -- as far as it goes. But anxious to add some depth to that perception, Greinert once discussed the problem with former U.S. ambassador to France Evan Galbraith.

"He told me, 'When you get to Washington, you can't be the press officer, you have to be the TV officer in order to change those cliche's,' " Greinert recalls. "I said I would not change but that I would take the old cliche's and add something new."

One of the "new" additions is an 800 toll-free telephone number appearing at the end of each series segment so that viewers can call the Austrian Embassy here about everything from skiing to Austrian goods available for import.

Says a jubilant Greinert, who tallied 240 calls after the first two programs: "Everybody's been calling!" The Embassy of Lebanon is using another approach to upgrade its image, a Nov. 21 by-invitation-only gala at the Kennedy Center starring entertainers of Lebanese ancestry.

"As time has passed, more people have, understandably, begun to argue that Lebanon has lost some of its magic. However, all agree that Lebanon has not lost and never will lose its soul," Lebanon's Ambassador Abdallah Bouhabib recently wrote hundreds of Washington officials and members of the media inviting them to the show.

According to Bouhabib, the gala is part of a larger effort to show the "civilized face" of Lebanon. "People have heard a lot about Lebanon, about the bloodshed, the terrorists, the war, but not about the other side, the cultural melting pot and how proud we are of our people who are entertainers, in government, in business."

Bouhabib and a group of Lebanese Americans came up with the idea of the gala this summer. Financed with private money ("Lebanon's government can't afford it," says Bouhabib), the show's organizers include entertainer Danny Thomas and Lebanon's consul general in Los Angeles, Tony Chedid. Besides Thomas, others expected to perform are actor Michael Ansara, singer Paul Anka and deejay Casey Kasem, to name a few.