On a recent morning at Chicago’s new Obama Presidential Center, the institution’s leadership discussed presidential papers the way a decluttering convert might talk about some old sweaters they tossed because they did not spark joy. The campus contains many features sure to delight the misty-eyed visitors who will flock here once it opens, on June 19: a museum that can come across like a pep talk from a more hopeful time; a light-filled basketball court; a whimsical playground; a public library.