In Canada, a free museum is very rare indeed so I am always delighted when I visit one of the many free museums and galleries in the United States. The Cleveland Museum is a beautiful space with a great covered atrium with trees and tables and space for kiddies to run around. (Reminds me of the National Portrait Gallery in DC)
The food service is great - lots of colleagues from Case Western across the street come to the museum cafeteria for lunch.
The exhibits are well displayed and curated. I saw a number of important pieces that I was familiar with from the impressionist and surreal school and was introduced to some new artists in the modern and contemporary section. I zipped through the historical art a little quicker - the indigenous Americas art was quite good, though I have to say that the gallery with Central Asian/Middle Eastern textiles was one of the most memorable.
If i have one quibble, it was that the gallery seems to focus on providing a little something from every region/school/era, without any exhibits organized outside of these geographic and chronological selections. This approach makes it great for school groups but less so if you're looking to be challenged by new ways of looking at things or eclectic groupings.
Overall, this museum stands out as a very good middle-city museum along the lines of Richmond, Buffalo or Montreal but not quite as good as any of the former.