How's your city doing these days? For the 5,000 officials wrapping up meetings in New Orleans with the annual convention of the National League of Cities, the question is hardly inconsequential. Despite a brisk economic recovery, many communities in the United States remain strapped for revenues, are slashing back services, and will have budget deficits right into next year. In short, many cities need a hefty rejuvenation of citizen - and federal and state - support.
That is not to say that the picture from the nation's cities is totally negative. Far from it. In some towns, progress has been made. Many communities have turned once-neglected downtown areas into vigorous new retail centers, such as the South Street Seaport in lower Manhattan. Or Faneuil Hall in Boston and Harborplace in Baltimore. And soaring glass and steel office towers are still being built in a number of communities.
All the same, Americans would be remiss in ignoring the pressing social and economic problems of cities. As pointed out by Mayor Charles Royer of Seattle, president of the league, ''over the last two years . . . we (cities) have deferred investments, we slimmed down, and we have raised taxes almost to their limits.'' In one new survey taken by the league, more than half the cities indicate that they will continue to reduce services in fiscal 1984. Hunger and homelessness are major challenges. Equally troubling: Fiscal woes that were common to large cities last year are starting to crop up in medium-size and smaller towns. Some 64 percent of US cities will face budget deficits next year, up sharply from 43 percent in 1982. That is expected despite higher taxes. Local taxes have already risen 21 percent in the past two years.
What is to be done to help the cities?
* Cities need to consider bold programs. Some communities have found that by contracting out services, they have cut back costs - yet improved efficiency.
* Cities need to fight for their programs in Congress. For example, to what extent should federal lawmakers impose restrictions on the issuance of tax-exempt industrial-development bonds, used by municipalities to finance new commercial enterprises? Both the Senate and House are considering restricting these bond issues to help hold down tax losses. But such restrictions could be counterproductive, in the sense of denying local governments a needed option for promoting new industry - and thus creating jobs.
* Cities need to strike a better partnership with business and citizen groups to restore downtown areas and neighborhoods. Another approach: urging Congress to provide special tax incentives to develop new industry in so-called ''urban-enterprise zones.''
* Cities need to modernize and rehabilitate discarded housing units. The federal government is not at present contemplating new public housing. Yet, the Department of Housing and Urban Development will help revitalize vacant older units that are so common to many cities.
Over the decades US communities have had a way of confounding all doomsayers - and constantly upgrading and modernizing themselves. Given the enormous talent and political and social vitality found in so many towns, there is no reason why today's challenges need prove any more insurmountable than those of past years.