Shortly near the end of our tour of the Smithsonian National Museum of Natural History I recalled that the Hope Diamond was probably at this museum. I knew it was in the hands of the Smithsonian and sure enough, this one made the most sense to be in. It's hard to miss as it's in its own single case and people flock to it like crazy.
It also rotates around to give everyone a fair view of the gemstone.
Honestly I was a bit disappointed, it's not really that beautiful despite its hype. There were plenty of other gemstones before it that were much more gorgeous.