Makes me dream of Project Orion
"Eight astronauts, with around 100 tons of equipment and supplies, could have made a round trip to Mars in 125 days."
Island One
One quarter the transit time equals one quarter the radiation exposure, and much greater payloads allow much better shielding, not to mention incredible scientific and exploration equipment.
I haven't found any figures for the actual amount of radiation released into the atmosphere (Shh, don't tell Johannes), but I think it would actually be fairly small.
Alas, politics and public phobias mean it will never happen.