Or a chess board, well to me that seems very museumish, checkered floor.

have you decided on which kind of museum you want it to be?
I can easily see a dinosaur skeleton hanging in the ceiling/standing on the floor.
Lots of small displays in glass boxes (history museum?/Asian sword museum?)
Or paintings on the wall, lit up with lights underneath or over.

Hmmm... I might try something like this some day soon

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