Unbuilt Washington". It is a 200 year plus retrospective of plans for the nation's captial that never reached fruition, like a Versailles-esque White House on Meridian Hill, a Smithsonian Gallery of Art with a shockingly modern design that would have replaced the Castle, a 200 foot tall water fountain for a Teddy Roosevelt Memorial (where the Jefferson now stands), and, the strangest by far, an elevated freeway around the perimeter of the national Mall. It's an amazing and often shocking look at what could have been and, for the most part, fortunately never was.
Part of the exhibit was dedicated to the tortured history of one memorial that has become so iconic, it's hard to imagine it never having been built. The Washington Monument was problematic from the start because President Washington had explicitly asked that no memorials be built in his name, wishing to avoid the godly hero-worship which had caused Europe so much trouble. But his wish was ignored and and, after many grand designs came and went, eventually a simple obelisk was built...over the course of 50 years, with the project stalling a third-built for 30 of those.
Now there is a plan afoot to rethink the design of the Washington Monument's plain, open field grounds. There is a public competition entering the final phase where you can vote on your favorite design. Some imagine a national amphitheater in marble that would hold 3,000 people, others a landscaped and wooded forest. You can see the entires here and vote on the site as well. Winners will be featured in the exhibit and their ideas presented to the National Park Service as they consider what to do with the grounds...after they fix the actual monument, still closed due to earthquake damage.