The word “museum” does not refer to a specific person, place, or thing. It refers to a type of place. Therefore it should not be capitalized.

Is museum a common noun or a proper noun?

On its own, the word ''museum'' acts as a common noun. As a common noun, the word ''museum'' refers to a general institution that houses pieces of...

Do you capitalize Science museum?

Proper nouns, such as the names of people, specific places (such as Mt. Fuji, the Atlantic Ocean, the Taj Mahal) need to be capitalized. You don't need to do it for generic places, such as a mountain or a river. The Science Museum is on Exhibition Street in London.