The Cleveland Museum of Art is one of the best kept secrets of Cleveland. It boasts a beautiful collection of paintings/sculptures and other art forms. It's most recent exhibit, from Monet to Matisse was exquisite. A beautiful depiction of the Impressionist era. We recently attended the NYE event there, nothing short of classy and fun.
The summer solstice is a must attend. If you are visiting CLE, definitely add the CMA to your list. It's a diverse cultural experience, and there's no entrance fee except for special exhibits. If you happen to be here on a first Friday of the month stop in for their MIXX events. Always aiming to attend to your novelty.