Museums don't have a characteristic smell, imho.
Libraries and archives do - old paper and bindings
slowly deteroriating give off a characteristic odor,
various photographic media have a distinctive smell
when they begin to degrade and there are lots of
smells one associates with individual collections
Mostly museums smell like the people who in the
building and their activities.

Way too frequently, the museum where I worked smelled
of hamburgers and other grilled foods prepared in the
large and very busy food court on the ground floor.
There was a special ventillation system and it may
have filtered particulates and smoke out, but the
aroma wafted throughout the building.

The other prominent aroma was that of "buttered"
popcorn -- there were popcorn vendor wagons set up at
various times and places.  On top of the popcorn for
visitor consumption, microwave popcorn was a popular
snack with lots of employees. It was reguarly prepared
in the "personal" microwave ovens that proliferated in
various departments and offices.

Ambrosia Chocolate used to make their product a few
blocks away from the museum, until either the City or
the Technical College acquired their property for a
parking lot and the chocolate maker moved out to the
'burbs.  Before that the heavenly aroma of chocolate
would scent the air outdoors when we left work in the
evenings.  It was delightful, but hell on diets.

Judy Turner
Whitefish Bay, WI