The ion drive exists

Not only does it exist, it is no longer considered experimental. Boeing offers the ion drive option on its 701 series communication satellites. (Power windows and tinted glass optional.)

The problem with the ion drive is its extremely low thrust. It is meant to build up speed by firing continuously for weeks or months. But it has essentially no moving parts, does not involve very high temperatures, and is fuel efficient. This makes it desirable for unmanned long-term missions. But many of the manuevers involved in landing on the moon require short-order changes in velocity which can only be accomplished by a powerful engine. So for now we're stuck with going to the moon on good old-fashioned chemical rockets.

NASA has, however, spent the last ten years experimenting with some radically different forms of propulsion. We may see something yet.