The Rock and Roll Hall of Fame is the city’s top draw, and with good reason. Its gorgeous building on the waterfront of Lake Erie is reason enough to visit. Keep up with events even if you can't visit - they live-stream public programs form their Foster Theater. See their website for details.
Great for youngsters is the Great Lakes Science Center.
The Cleveland Museum of Art has over 30,000 works covering 5,000 years of civilization, from the civilizations of ancient Egypt to our present day. You can see 144 highlights of their collection, masterpieces from around the world, at their online exhiblt.
The Museum of Contemporary Art houses an impressive collection, and plans soon to move to a brand new building in University Circle. This summer exhibitions feature the works of two New Yorkers: Marilyn Minter, who examines the relationships between the body, photography, and painting, and taps into cultural anxieties about sexuality and desire - through August 14th; and Aïda Ruilova, mixing classical cinema, popular culture, avant-garde music, and a do-it-yourself aesthetic, using single channel videos to create an evocative, haunting, and dissonant environment - through August 15th.
The Museum of Natural History has a collection of over four million specimens in the fields of anthropology, archeology, astronomy, botany, geology, paleontology, zoology, and wildlife in general. Through August 29th they're featuring Wild Music the sounds and songs of life on Earth. They also have ongoing programs on conservation and sustainability - with classes and programs to help keep the song alive.
The Botanical Garden is a collection of various gardens that include the first US Children's Garden, a Japanese Garden, and Rose, Herb, Perennial and Woodland Gardens; plus tropical plants in their Glasshouse. Open every day except Monday.