The idea is simple. There is a vast amount of space which remains to be explored by the telescopes. Why not allow the public to decide upon which area is captured next?
This mission comes to mind:
I'm afraid I have no idea of how expensive or difficult these images are to capture. But if you were to make it affordable (perhaps as a gift) to allow someone to point the telescope at an area of the sky (I imagine a google maps type interface), and capture an image I think it would be amazing for getting the public involved.
Not only would could you get the revenue from the picture capturing, but I'm sure there would be significant revenue from ordering prints as well.
I got my first telescope when I was very young because I was also so fascinated by these images. I'm sure I would have loved this as a gift. As a matter of fact, I believe I would still have the print framed in my room to this day.