Cleveland Museum of Art
This museum houses an excellent collection of European paintings, as well as African, Asian and American art. There are over 50,000 pieces in its collection, including a wealth of late 20th-century works by artists such as Andy Warhol, Jackson Pollock and Francisco Clemente.
The museum is currently undergoing a renovation and expansion which won't be completed until 2011. The entire permanent collection, however, will be back for viewing sometime in 2007. Check the website for details and news of the many arts events happening around Cleveland in the interim.
Great Lakes Science Center
The Great Lakes Science Center, next to the Rock Hall, is a cunning place to entertain your kids while teaching them about science and the environment. It has lots of hands-on exhibits, as well as an Omnimax theatre, and gives a good account of the lakes' environmental troubles.
Berthed nearby on the waterfront are the storied submarine USS Cod which saw action in WWII, and the William G Mather a freighter incarnated as a steamship museum.
HealthSpace Cleveland
While it's geared mostly to kids, HealthSpace Cleveland exhibits appeal to adults, too, especially the 'stress yard' and 'deli wagon' (showing how fast-food ramps up fat and sugar intake). Sneezes, by the way, can reach 100mph, and right-handed people live nine years longer on average than left-handed folks.