My very favorite museum is The Anthropological Museum in Mexico City. It is amazing collection of the history of Mexico and a true testament to the creativity, talent, and vision of the indigenous people of the land. It is a wonderful reminder to me to never underestimate or discount the value of another just because he/she may look different, speak differently, or worship differently than me.
I am also a big fan of the Museum of Natural History and the Field Museum. What makes them special to me is that I shared them with my son and was able to experience both through his eyes.
While, technically, not a museum, I would include the city of Philadelphia on my list. I love to be able to see what life was like in different times throughout history, and I appreciate the efforts to preserve so many buildings/places where America was born.
I also love the Arizona-Sonora Desert Museum. I did not appreciate the landscape of the southwest when I moved here. This museum opened my eyes to the beauty of the desert. I no longer think of of it only as being brown!