The nuclear interplanetary shuttle has no mission, nor will ever have a mission worth the trouble.
Agree with the mining of asteroids. Disagree that such a shuttle would be worthless. First off its design could be the framework for a space truck for getting mining spoils back to Earth, or Moon, or where ever they would be processed. Two, there are no doubt other bodies to be explored and resources to be retrieved from other areas of the solar system. Why not have a nuclear powered craft that doesn't require the massive amounts of conventional fuel now used?
If there were a manned base on or orbiting Mars, a nuke shuttle might be convenient to reduce transit time for the crews, but not necessary.
Aside from those two uses, I don't see commercial viability for the nuke shuttle.