Nashville — Few governors like to admit it. But most here for the midsummer meeting of the National Governors Association (NGA) know they can afford to indulge in an occasional smile these days.
They are here to discuss tough state problems such as unemployment, illegal drug trafficking, and toxic waste dumps. But as Wisconsin Gov. Anthony S. Earl (D) observes: ''Because it's a political year, I think an effort has been made to put together an agenda which is not controversial.''
Accordingly, the mood here is relaxed, with host Gov. Lamar Alexander (R) of Tennessee launching the first evening's festivities by sitting down to play Grand Ole Opry's piano.
In many ways things have been going better for the nation's governors as a group than in some time:
* Most of them watch over state budgets that are in much sounder shape than is the federal budget in Washington. According to a recent NGA survey, the improved economy, tax increases, and spending cuts have combined to help the states end fiscal 1984 with a collective balance of more than $3 billion.
* Many governors in recent years have launched bold initiatives in everything from educational policy to environmental projects. Many of the ideas have been picked up by other states and by Washington. And the governors' collective prodding is considered crucial in getting issues such as the rising federal deficit on the agenda for public discussion. ''I think the governors are generally more upbeat than a year ago,'' says Governor Earl. ''But most of us are feeling much more cautious than the national administration about the future of the economy - there's still a good deal of nervousness.''
* Only 13 governorships - six held by Democrats and seven by Republicans - are up for election this year. That smaller-than-usual number is the result of a bipartisan effort by most states in recent years to separate the timing of state and presidential elections to avoid any coattail effects. And governors' terms are getting longer. Only four states still have two-year terms.
* Also, governors are more apt to be considered as presidential candidates these days. That was the case for much of the first half of this century, but during the last 30 years it was more often US senators who moved from within Washington from Capitol Hill to the White House. But the elections of former Georgia Gov. Jimmy Carter and former California Gov. Ronald Reagan could signal the beginning of a return to the old pattern. One possible beneficiary: New York Gov. Mario M. Cuomo, who delivered the stirring keynote speech at the recent Democratic convention. But he will get no springboard for a 1988 presidential run at this conference: His only scheduled appearance is a speech, closed to the press, on nuclear-plant cost overruns.
University of Virginia political scientist Larry Sabato says governors are exceptionally well-equipped to serve in the White House and have tended to make the best presidents. In his view, state executive experience, including the relationship of a governor to a legislature, is much better training ground for the job in the Oval Office than is legislative experience.
''Whatever you think of Reagan as president, he's done surprisingly well with Congress, and he's a wonderful delegator,'' says Mr. Sabato, author of ''Goodbye to Goodtime Charlie.'' ''He learned in California that an executive is most effective when he keeps his personal agenda small. Jimmy Carter never learned that in Georgia. He was overwhelmed by detail.''
Sabato says today's governors are younger, better educated, more thoroughly trained (often lawyers or businessmen with legislative experience) than those of a few decades ago. And most are more interested in the substance vs. the ceremony of their job than their predecessors have been. University of North Carolina political scientist Deil Wright agrees: ''Most governors aren't interested in the job for show. They want to do something.''
Although the NGA is currently heavily Democratic - Republicans are outnumbered by more than 2 to 1 - its meetings have traditionally not been sharply partisan. Still, with six governors seeking reelection, and two - Democrats James B. Hunt Jr. of North Carolina and John D. Rockefeller IV of West Virginia - running for US Senate seats this year, no one expects politics to run too far below the surface.