One of my favorite exhibition spaces is actually the Louvre and the Statue of Nike. You have to ascend a few flights of stairs, all while staring up at a magnificent headless statue of the winged Greek goddess of victory. It has an incredible amount of natural light, and the surrounding stone is of a warm, light shade that allows the even paler statue to stand out. Even in the tightest of crowds, you can still see the statue fly above everything else.
For me this space is one of the most interesting because of the natural way it draws your focus to the piece, both through physical travel and the contrast between the surrounding environment and the piece itself.
Another space I really liked was the DeYoung museum in SF, mainly because of the unique building skin. It brings the art from the inside to the outside park and really adds to the landscape around it. I think exhibition spaces are different from other buildings specifically because they are meant to show off. This means there should be more creative license with the exterior design to hint at the display inside. In fact, the exterior can even be used as part of the exhibition.