The nation's governors went to dinner at the White House last night and at least one of them made no bones about the fact that he was casing the joint.

"I'm just looking the place over, that's all," said Massachusetts Gov. Michael S. Dukakis, fresh from his New Hampshire primary victory by way of Georgia and Texas, with stops coming up in Minnesota and South Dakota today and tomorrow.

Dukakis, in town with his wife Kitty for the National Governors Association's winter meeting, was the only presidential candidate at President Reagan's farewell dinner to the governors. But Dukakis almost certainly was the last person Reagan had in mind when he toasted his guests.

"It's not the last time for you, but it is for us," Reagan said nostalgically of the annual White House dinner.

He also sounded a couple of favorite themes. "The best government of, for and by the people is not national government, but state government," Reagan said at one point. At another, mindful of the balanced budget requirements and line-item vetoes some governors have, he said: "Not one of you would put up with the mess that we have here in Washington at budget time."

New Hampshire's Republican Gov. John Sununu, as chairman of the governors association, noted the passing of an era in his response to Reagan, when he spoke of the "true affection for someone we have come to like and love."

"From all of us to one of us: You did it your way; you did it well. God speed," Sununu added.

Later, over coffee, Reagan told reporters that the administration was "exploring every avenue" to gain the release of U.S. Marine Col. William Higgins, taken hostage in Lebanon last week. "It's just so difficult. We don't know who has him and where they are," Reagan continued, asking reporters, "Why don't you, when you start talking about the terrorists and the kidnapings, why don't you start calling them cowards?"

He said, "They all make me mad. I just feel that any time a citizen of this country is denied their constitutional rights, it's the obligation of this government to come to their aid."

Meanwhile, back on the campaign trail, Dukakis, on his side of the Blue Room, jokingly replied to a question about how he liked what he saw of the White House: "I've never lived over the store before."

When a reporter relayed that remark to Reagan, he was only momentarily the upstaged actor, coming back with the quip, "I've used the term a number of times because I did live over the store as a kid."

Dukakis managed not to sound too confident about his New Hampshire win.

"Steady as she goes, you know," he told reporters. "So far so good. Two more on Tuesday and 20 two weeks later," he said, looking ahead to upcoming primaries, including the Super Tuesday slate on March 8. "... This is going to be a long one."

Tennessee Gov. Ned McWherter conceded Dukakis' regional strength but said that in Tennessee it will be Sen. Albert Gore Jr. in the No. 1 spot on March 8, with Jesse Jackson coming in second.

He also said Super Tuesday isn't focused yet in the Southeast.

"They haven't followed the elections very closely {there}. The men and women who really vote go to work every morning, get the kids off to school," McWherter said.

Mississippi's newly elected governor, Ray Mabus, said the primary election there March 8 is so new that "it's real unclear who's going to vote in which primary. We don't have party registration in Mississippi, and the last poll that I saw showed that 20 percent of the voters that say they're definitely going to vote don't know which primary they're going to vote in. So it's hard to get a handle on it."

Another state holding its first primary on Super Tuesday, Virginia, will be "wide open on both sides," said Gov. Gerald Baliles. "I think Iowa and New Hampshire really did not settle anything in terms of establishing clear winners."

He said there will be "a lot at stake, but given the different level of politics -- retail politics predominated in both Iowa and New Hampshire -- Super Tuesday is going to be wide open, wholesale politics."

On the Democratic side, Baliles predicted Jackson, Gore and Rep. Richard Gephardt would prevail in his state, with Dukakis faring better in Florida, Texas, Georgia and North Carolina. As for the Republican race, he predicted Pat Robertson, Vice President George Bush and Sen. Robert Dole would be "fighting it out."

South Carolina's Gov. Carroll A. Campbell Jr. was more certain, predicting a Bush win in the South but only after a showdown with Robertson. He all but wrote off Dole.

"Dole made some statements today that he doesn't think the South is that important. As a result it's turned out to be Bush and Robertson, and I think Bush will win," Campbell said.

In the north, South Dakota's Gov. George S. Mickelson saw it quite another way.

"Senator Dole is going to do very well in South Dakota. He's been there a lot of times -- he's been there the last couple of years, in fact while I was campaigning for governor," said Mickelson.

The Dave Brubeck Quartet entertained in the East Room after dinner, playing a musical tribute to Black History Month and the musicians "who taught me so much" with numbers that included W.C. Handy's "St. Louis Blues," Duke Ellington's "Take the A Train" and his own classic, "Take Five."

The applause was thunderous, and at the end brought the audience of 44 governors, their spouses and several Cabinet officers to their feet.

"You don't get many standing ovations in this room," said Elaine Crispen, Nancy Reagan's press secretary.

"It is magic," Reagan said from the stage where Brubeck, his son Chris on bass guitar and slide trombone, Bill Smith on clarinet and Randy Jones on drums surrounded the first couple. "I know it's sort of a cliche' but they not only don't write 'em anymore, there aren't very many around who play them that way anymore."