A friend told me he remembered Albert Ducrocq (french science journalist at a commercial radio) saying that "tonight, you'll be able to see the Saturn SIVB-Apollo stack leaving LEO at Trans-Lunar Injection from your home at a certain moment" and that's what many witnessed!
Wouldn't it be great to see a manned spacecraft on its way to the Moon? I'd love it!
But for instance, a CEV atop a Delta 4 rocket could send astronauts around the Moon and back in 7 days. Would anything be done to attract the public a little more?
A government project would be more interested in testing some systems than in a pure stunt. Perhaps a stunt can be added and be presented as a system testing: I think about a spacewalk , untethered, performed away from the spacecraft and while the astronaut and the spacecraft are flying by the Moon, behind it.
The spacewalk could be meant to test the spacesuit for a 10 hour long EVA, test the astronaut while floating in space further away from the Earth than anyone before (a stunt there too), have an Imax camera (attached to him) taking a movie from that distance. Test a Manned Manoevring Unit that could be used for astronauts to study Near-Earth-Asteroids. Test a system enabling the astronaut to find his way back to the capsule even if it's kilometers away. And to add (a stunt), have the astronaut handle a mirror in such way that people on Earth can see him when he reappears from behind the Moon.

The thing is: stunts seem to have no real purpose other than being stunts, but they could be argumented into a test object for later missions.

As for commercial manned spaceflights, going from a ballistic flight to an orbital one sems much much more difficult than from Earth-orbit to Trans-Lunar Insertion. Could tourists be ready to pay for and industry ready to commercialize a rocket and a spacecraft capable of leaving LEO for such a trip?

Raoul