Washington DC - National Air and Space Museum
The National Air and Space Museum - a museum so large, it spans two (public) locations. (One of which isn't actually in DC.) Where other museums might hope for a few grains of moon dust, this one has multiple Apollo space-suits still grubby from astronauts bounding around the lunar surface.

If it's a spacecraft, they'll either have a flight spare (the spaceborne versions being currently inaccessible) or the real thing should it have returned to Earth. Such as the Discovery Space Shuttle...
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