Los Angeles art adviser and collector Elaine Gans was uncertain, at first, where to donate a large painting by San Francisco Bay Area artist Tom Holland. It was “one of his most important pieces,” Ms. Gans says.

If she gave it to an art museum, the painting risked being put in storage and forgotten, Ms. Gans says. A museum also might not have accepted it, she adds. So, earlier this year, she donated the painting to Cedars-Sinai Medical Center in Los Angeles.

It’s...