For someone like Milton D. Tutwiler, Washington D.C. - with its billion-dollar-a-year budget, its brand new subway system, its 44,000 employees and, most importantly, its black mayor - has got to be a fascinating place to visit.

At the ripe old political age of 28, Tutwiler already has behind him two and a half years as chief of police and is now the newly elected mayor of Winstonville, Miss., (population: 536).Like the mayor of the District, Tutwiler is black.

Winstonville is one of the those dirt-poor towns in the Delta country of Bolivar County, Miss. It has an annual budget of #17,000 (less than the yearly salary of a GS-11). There is no city hall. The entire city can fit into the grounds of the District's massive Blue Plains sewage treatment complex three times and still leave enough room to park a couple hundred cars.

And Winstonville collects only about $700 a year in property taxes, Tutwiler said, partly because half the land in the town is owned by whites who don't pay any property taxes to the government of the virtually all-black city.

One day last week, Tutwiler, along with about three dozen other visiting black mayors, was standing behind a glass screen at the Metro operations center here, watching little white dots march across the television monitors that show how trains on the subways system are moving.

"Mayor, what's the biggest transportation problem you're facing in your town," a reporter asked Tutwiler.

The mayor smiled and grunted a short laugh. "We don't have a single street in town that's paved," Tutwiler said! "We're poor. I'm the poorest mayor in the Delta. We don't even have a typewriter to send off a decent letter."

Although his situation is admittedly a little worse than average, it is closer to being typical of that faced by most of the nation's 161 black mayors than is the situation here. This city is by far one of the largest in the country run by a black mayor. Most cities with black mayors have populations of 3,000 or less and are largely located in the rural South.

It is in that context that D.C. Mayor Walter E. Washington was the host to more than 100 of his colleagues last week at the National Conference of Black Mayors, meeting at the Sheraton Park Hotel. Walter E. Washington was undisputedly the king of the hill, and he loved it.

The meeting was a chance for the city's often criticized government to show off. It was a time to forget about the usual accusations of inefficiency, ineffectiveness and rampant cronyism. The main thing most of the visiting mayors knew about Joseph P. Yeldell, for example, was that Yeldell helped put the meeting together and without him it might not have gone on.

It was also a time to occasionally ignore the limited powers of this city government (Tutwiler has more control over his tiny budget than Mayor Washington has over the District's) and to concentrate instead on the relatively positive side of local goverment in Washington.

Not only as the host mayor, but also as one of the few big city mayors present, Mayor Washington became a genuine center of attention with his impressive, chauffeured black limousine with the D.C.-1 tag and his ever-present bodyguard.

The mayor hosted a reception for more than 500 people in the Sheraton Park Hotel ballroom, and Mrs. Washington had her own reception the following afternoon. The mayor spoke at both the opening and closing press conferences. He addressed the opening session, and he presented the organization's first annual Fannie Lou Hamer Award to Coretta Scott King, who was standing in for United Nations Ambassador Andrew Young.

At week's end, no one on the mayor's staff could say how much it all cost. But the Conference is strongly considering meeting here every two years, and Mayor Washington is now on the organization's executive committee.

Some D.C. city officials are hoping to export their technical advice to assist the small cities in learning how to manage their affairs. The mayors adopted unanimously a resolution supporting full congressional voting representation for the District and promised to help get the necessary constitutional amendment passed by their respective state legislature.

Politically, it didn't appear to have, hurt the mayor. Fresh from what some viewed as a people-oriented victory in the city's rent control war, there was the embattled mayor of the District amidst his colleagues, his peers, receivint their praises for his hospitality and plaudits for his administration.

"One of the things that does concern us," said Mayor A. J. Cooper of Prichard, Ala., the president of the organization, "is how black politicians in general and some of our mayors in particular, as they stand up for more resources, have become identified as symbols to be crushed."

The audience of mayors applauded, television cameras whirred, Mayor Washington flashed a grin, and later he generously thanked the press for dropping in to listen.

Last week was apparently the time for filing disclaimers about future political plans.

David Clarke (D-One) was for about two days interested in running for an at-large seat on the City Council next year. However, Clarke quickly withdrew his trial ballroom when it became clear that Marion Barry seems dead set on challenging Sterling Tucker for mayor in 1978. Clarke said he would only run at-large if there were a unified Democratic slate, and a Barry-Tucker faceoff does not suggest such unity. Clarke says he'll stay where he's at.

John Wilson (D-Two) has not only cancelled his previous interest in running for mayor in 1978, but also announced that he will not run for council chairman, won't run at-large and disowns any efforts to draft him for any of those posts.

Wilson wants to set the record straight so no one will come along holding the city election law in his face and asking him to resign his present seat early because he's become a candidate for another office.