It seems my response to anything nuclear ends up being, "Just use solar." And so it is, yet again.
You can build a type of rocket called a solar moth that can achieve similar specific impulse (Isp) as a liquid core NTR (which is what is being described here) but is much lighter than any NTR because it doesn't require heavy neutron shielding (you can only really shield neutrons with high-Z atomic nuclei, and thus mass; that's why lead is a great neutron shield). Using non-Hohman trajectories, i.e. dropping inside the or bit of Venus first to double your specific power and then meet up with Mars on the back leg, you can reach Mars inside of 90 days.
Mars orbit gives you only 44% of the insolation (incidence of solar radiation) as Earth orbit. You can overcome this easily by including two extra mirrors to double the collection surface area of the engine. This won't add much weight as most of the mass of the engine is going to be in the heat exchanger and nozzle of the engine. In the inner solar system, the rocket isn't so much limited by the collection area of the primary mirrors but by the material thermal limits of the heat exchanger. If you were using unobtanium instead of real matter in the heat exchanger, you could achieve temperatures equal to the temperature of the surface of the Sun with clever engineering.
With a solar moth, round-trip time for a "Flags & Footprints" mission is 6 months. We actually do know how the human body will respond to 0g for that length of time from Mir and ISS.