What NASA should do that would amaze even the simplest layman.
I got this idea from the recent XKCD with the 100 foot apart cameras.
Put two very large deep field telescopes at the L2 and L3 Langrangian points. (If you didn't know, L3 is behind the dark side of the earth, and L2 is directly opposite the earth, on the other side of the sun; they're points of earth-sun gravitational equilibrium.) Sync them to be parallel to each other, and use them as eyes. Put the streams together in a 3D cinema viewer. Real time.
This could mean that thousands of people from across the globe could sit, with personal glasses or on a large screen, and see the near universe, in 3D, live.