The president and Mrs. Reagan began a marathon of ball-going last night with a visit to the American Legion's banquet in a capital celebrating both the inauguration and the hostages' freedom.

Maureen Reagan showed up about 10 at the Mayflower Hotel Youth Ball, right after the Pointer Sisters, the evening's entertainment. She had her fiance in tow, and told the crowd to have a "wonderful evening and a terrible hangover.

"You're great," she said. "We love you." The crowd cheered lustily.

The president, who came 10 minutes early, at 8:50, spoke of a "new era" and got as many cheers as his daughter. Vice President Bush showed up late, his entrance delayed by a bomb threat, phoned into the Mayflower Hotel shortly before 11. He was last, but he certainly wasn't least in the hearts of his young admirers. "I'll tell you something, this is a great day. This is a new beginning for the U.S. in foreign policy," said Bush. "Never again a Tehran." This time the crowd roared.

Oh, to have been young and Republican last night at the Mayflower, where the inaugural committee hosted the ball designated for the 18-to-30-year-old crowd. More than 3,200 of the young and the restless, decked out in black tie and spangled gowns, ebbed and flowed throughout the hotel ballroom, as the singing sisters shook and shimmied on stage.

"Dig it," said Rich Stewart, 21, from Des Moines. "This place looks more crowded than the San Francisco Freeway."

"I was here four years ago for the Carter ball, in this very same room," said his companion. "That wasn't a party. This is a party."

George Bush called the nine-ball evening "cruel and unusual punishment," but few at the Mayflower would have agreed with him. "This is a great reward," said Jefferson Power, a "Law School Republican" from Malibu. The room was full of people who called themselves Young Republicans, College Republicans, or Law School Republicans, depending on their age. "The Reagans are great," said Power. "My roommate helped them move out of the ranch the other day -- he carried out some of that Gucci luggage. Washington is so exciting, and so different. Even the girls are different here. They're more traditional; they're more formal. I mean, in California, everyone wears bathing suits."

There were so many ticket holders that many were left standing in the crush outside the ballroom, as District fire marshalls attempted to keep the dance floor from overflowing.

The crowd was young, but few were as young as a social studies class of 27 eighth graders from Ridgefield, Conn., who came to Washington for a whole week -- "with their own money" -- and stood in clumps around the room, sipping ginger ale. They weren't dancing much, mostly because the boys, who stood in a tight circle, weren't asking.

George Bush stayed only minutes, as did the Reagans, but his buoyant address left some in the crowd pleased indeed. "The Bushes are grateful to be a part of this, and grateful to you for your part," said Bush.

"This country needs to get back to the traditional values," nodded Tom Scott, a Young Republican from UCLA. "We have to be respected. I worked for George Bush in the primaries."

"A lot of us here did," said someone else. "He could go all the way."

"Yeah," said a third party. "He and Senator Maureen."