Two of the exhibition spaces that I've really enjoyed are: the Museum of Islamic Art in Doha, Qatar and the British Museum in London, UK.
I'll start with the Museum of Islamic Art — the setting and surrounding landscape of the building was just beautiful. The look and the feel for the entire building just fit right into the landscape and was formed a pretty good combination between man-made and natural elements. The choice of stone colour was a fitting reminder of the desert that surrounds the city. Combined with the edges and big blocks that formed the building, I was just really impressed with the overall design of the structure. The huge open spaces at some places outside of the museum was really nice (there were fountains and it overlooked the sea and the city skyline). The open spaces indoors are also really nice — when you first enter the museum you're greeted with a huge open space that directs your eyes towards the giant light structure hanging in the middle of the room. It lights up the entire place and the symmetry of the building is beautiful.
The British Museum — the atrium that you're greeted with when you first walk in the building is absolutely phenomenal. I was blown away just by how big it actually was. It made me feel tiny and it was crazy to see so many people walking around the museum. For the individual exhibits inside, I really liked the lighting that they put for each individual item. The space given for each item helps to emphasize importance for each historical item. I also love how there's just twists and turns in the museum that can really take you anywhere (although that is a common feature of many museums I think that's why it makes them effective and popular). The isolated environment (somewhat dark in the exhibits but bright in common spaces) helps the individuals to sink into this mindset to really discover what kind of artwork / historical pieces are being presented.
I would say the primary factors for these being memorable to me are the aesthetics and the physical impressions that the places provided for me. Lighting is also an extremely big factor. Overlooking expansive landscapes helps to integrate the building into the natural environment.