I fell in love with art at the Cleveland Museum of Art when I was attending school nearby. It's not the MFA or the MOMA, but it's a very solid museum.
4 stars only because most exhibits are closed until 2012. I miss the garden and the egyptian exhibit. It looks like it will be amazing when it comes back to life in 2012.
I would still absolutely recommend that you visit this gem anytime you can. It's such a beautiful building and such a relaxing place to visit. Oh, and did I mention it's free?
Do not miss "The Thinker" & the wade lagoon while you're there. They're behind the art museum and the thinker is one of their coolest pieces. Obviously it's one of many, but this one is special because it was damaged some time ago. I find it really cool to look up inside the casting and see what it's all about. It looks like a few sticks of dynamite went off underneath it. Go see it!