Among many other achievements, Lindbergh made the first successful transatlantic flight from the U.S. to Europe in 1927.
Baldwin said his initial introduction to Armstrong was preceded by a chiding from his grandmother after he had ventured to an upper floor of the Explorer's Club with his aunt while everyone was arriving.
"My grandma came up there mad as fire," he said. "She said, 'Neil Armstrong is down there! Get your butt down there!"
Williams said he sat his grandson next to Armstrong at dinner so the two could have a conversation.
"I just wanted to make sure that Trey was able to experience that because I'm trying to get him interested in aviation," Williams said. "I like the opportunity to get to take him and do these things."
While dining on food that was a mouthful just to pronounce — like "petite savory crostini topped with port scented figs, goat cheese and toasted almonds with honey balsamic vinaigrette" — Baldwin got the chance to ask Armstrong about a particular scene in the movie version of the Apollo 13 mission.
Baldwin asked if Armstrong had really visited Jim Lovell's mother while Lovell was on the mission.
Armstrong said yes, he had visited Lovell's mother, but the movie got it wrong when it showed her asking who Armstrong was. Armstrong had known Lovell's mom since he was a young boy, he told Baldwin.
Besides the Lindbergh Foundation celebration, Baldwin got to see the Statue of Liberty (from his plane as he flew into New York), took a bicycle taxi ride (at $40 per person) and explored Times Square and the Empire State Building. He even stumbled across someone you would likely only ever stumble across in New York City.
"I was looking down at my iPod, not looking where I was going … all of a sudden I wound up in the middle of a huge circle of people," he said. "We saw the naked cowgirl and I was standing right there next to her."
Williams said he's optimistic the achievements of the astronauts his grandson got to meet will inspire him to do great things.
"It was actually very, very extraordinary and I'm sure it was great for Trey," he said. "Maybe one day he'll change the world, too."