The model sits aside other significant artefacts from the history of flight and space exploration, including Sputnik, an Apollo lunar module, and SpaceShipOne.
TrekCore have visited the display, and have a good gallery of shots, including this view of the rear, which in contrast to the other side, make's the model's use from television production obvious. The original stand is also on display. You can get a good look at other exhibits in the hall in a good report from Collect Space.
And here's a beauty shot from the Smithsonian:
The Smithsonian have also posted a new article detailing the final stages of the Enterprise's restoration, including details of the final paint work:
Then the whole model (minus the upper saucer paint, of course, which is original paint from the 1960s) was painted with a base color that had been carefully matched by the Museum’s Dave Wilson to the production base color that had been uncovered in multiple places on the model in sanding tests.
Kim’s first step was mixing the colors that would be used for the weathering, details, and markings. The detail paints were mixed to match the colors that Dave had carefully revealed, and were adjusted and balanced for appropriate contrast and intensity based on comparisons with the historic images.
A full-scale mockup of several of the model’s parts (nacelles and secondary hull) provided a way to test paints, techniques, and finishes before applying any paint to the actual artifact.
Finally, it has also been announced the Smithsonian Channel will been screening a two hour special looking at the restoration of the Enterprise, and the influence of Star Trek on technology. It will air on the 4th of September. This is how it was summarised in a press release:
BUILDING STAR TREK will follow the conservation team from the Smithsonian’s National Air and Space Museum as they attempt to restore and conserve the original 11-foot, 250-pound model of the U.S.S. Enterprise from the original series. The special also will track the effort to rebuild a model of the original U.S.S. Enterprise bridge by using authentic set pieces and props, which recently went on display at Seattle’s EMP Museum.
The two-hour special also profiles a new generation of engineers and scientists who are making Star Trek’s visionary technology real, pushing the boundaries of physics with inventions first conceived on the iconic series: warp drives, medical tricorders, cloaking devices and tractor beams. Proving that one TV show has truly gone where no man has gone before, BUILDING STAR TREK will showcase clips from the original series that highlight each scientific innovation and the new technologies that have inspired generations.