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.

Even before the Peter Duchin Orchestra struck the first note at the ball at the Shoreham Hotel last night, Christopher George, an 11-year-old from Queens, pronounced the evening a success. "This is great. I just wanted to get to see the president," said George, whose father, a lawyer, and whose mother, a judge, watch another New York Republican take his picture.

Like so many others, the Georges weren't worrying about the expenses, $400 for last night's tickets, $300 for their Holiday Inn rooms, and all the auxiliary costs. They felt they were part of history. "Last night we were in a cab with a young woman who said she had to get to the Federal Reserve Bank in a hurry. When we got a block away, she was so frantic she jumped out of the car and ran," said Norman George. "And when we read about the hostage deal in the paper this morning, we felt good about taking her to the bank first."

Edging out some space for themselves at the edge of the crowded dance floor were four Orthodox Jews wearing black tuxes and satin yarmulkes. Rabbi Moshe Harfenes of Brooklyn said they were getting together a new strategy for their next political campaign. "We were all native Democrats, but switched because of our discontent with Carter's Mideast policy. Now we're going to campaign against Gov. Hugh Carey, because he's against the death penalty." The four exchanged slips of paper and then fanned out into the dancers.

By the time the Reagans arrived (eight minutes early), the crowd was shouting. Some loud voices demanded that Nancy Reagan speak, and she did -- briefly. After the rocket-fire, 10-minute visit, the crowd lined up for autographs and pictures with Treasury Secretary-designate Donald Regan, CIA director William Casey and New York Rep. Jack Kemp. With Anthony Newley shouting the theme from "goldfinger" in the background, Kemp said, "I'm thrilled I've been the one that's tried to sell the Republican view that unemployment is inflationary."