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“The main thing that Michelle and I contributed was just saying, ‘What is it that we want to see 10 years from now?’” he said, recounting his conversations with the architects who designed the center. “And we don’t want to see some big building that’s dead, and kids are getting dragged to it for a field trip. What we wanted was something that was alive, and that was a hub for the community and for the city and for the country.”

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The Obama center could be one of the biggest projects ever developed on the South Side, at a cost of at least $500 million. Expected to be completed in 2021, it will be located in Jackson Park, a space designed by Frederick Law Olmsted. The 500-acre, lakefront park already includes the Museum of Science and Industry, a beach, golf courses and athletic facilities.

Mr. Obama said he wanted his library to include a children’s play area that would attract families from the neighborhood, and a community garden for schoolchildren. He said he wanted food trucks and some grills so people can barbecue, prompting chuckles from the crowd.

“Why are you laughing?” he asked. “We don’t have any folks who grill here? I thought this was the South Side of Chicago!”

Because Mrs. Obama lamented that Jackson Park did not have hills when she was a child growing up in the nearby South Shore neighborhood, Mr. Obama said the presidential center would be outfitted with a sledding hill.

Mr. Obama said he envisioned “a studio where I can invite Spike Lee and Steven Spielberg to do workshops on how to make films,” and “a recording studio where I could invite Chance or Bruce Springsteen, depending on your tastes, to talk about how you could record music that has social commentary and meaning.”

“What we want this to be is the world’s premier institution for training young people in leadership to make a difference in their countries, in their communities and in the world,” he said.