Hoping to show off Washington as a city of monuments rather than one of monumental problems, the District's Democratic establishment sought to charm a gathering of national Democratic leaders last night at the new convention center, saying the capital is just the place to hold the 1984 Democratic National Convention.

"Isn't this a magnificent facility? It's a natural," said a beaming Mayor Marion Barry as several hundred people crowded into the center to eat and drink alongside a 60-foot-long diorama of the Lincoln Memorial, Washington Monument and Capitol, complete even to two tin-foil reflecting pools.

"It's the shortest distance to the White House," joked John Hechinger, D.C.'s Democratic national committeeman.

The reception for members of the Democratic National Committee, who are meeting in Washington through the weekend, was actually aimed at the 1984 site selection committee, which held its first meeting yesterday.

"There's no question people want to go to San Francisco," said Melba Williams of Georgia, who acknowledged that Washington is "nice." But, she added, many Democrats are convinced that San Francisco has the inside track over Washington, Detroit, Chicago and New York. "We have to keep an open mind," she said.

The District, which submitted its proposal on Jan. 28--just 30 minutes before the deadline--is making what even local officials agree is a long-shot effort to win the site committee's favor.

"We're going all-out," Barry said. City officials said the budget for securing the convention--which could mean millions of dollars pumped into the area's economy--probably would top $100,000 before the decision on a site is made April 28. The costs are being picked up by the city and private businesses.

Before the choice is made, about 60 members of the site selection committee and technical advisers will tour each of the cities--at the individual city's expense--during late February and March.

If Washington is selected, "I will get my street fixed," joked the national Democratic Chairman Charles T. Manatt, who lives in Georgetown but is said privately to want the convention in San Francisco.

Democrats were taken to the convention center on double-decker buses that featured open bars and waitresses. They were treated to videotapes of speeches by former presidents John F. Kennedy and Franklin D. Roosevelt, while hallways were lined with cheering youths carrying placards touting Washington as "America's hometown."

A band played and city officials stalked the crowd looking for receptive committee members. Most of the members declined to comment publicly on their site preferences.

Washington is 70 percent Democratic and is bordered by the states of Maryland and Virgina, both of which have Democractic governors, Barry pointed out during the course of the evening.

Barry also said the city has one of the nation's best transportation systems and most plentiful supply of hotel accommodations.

Some labor officials said the convention center, which has about 85 employes, is now nonunion, and warned that it may be a drawback with the prounion Democratic Party. However, aides to Barry and Joslyn Williams, head of the Metropolitan Washington Council, AFL-CIO, said the issue probably would be settled and have no impact on the selection.