What you are describing is a VTOL aircraft, not a hovercraft. I suspect you want the rotors to be enclosed, rather than open like a helicopter, which would make operating in urban environments a bit easier, since there is little risk of the rotor blades coming into contact with the buildings.
Why nuclear power isn't used in aircraft is the crappy power to weight ratio. Nuclear energy is extremely energy dense, but the ionizing radiation and neutron release of a fission reactor will quickly kill the passengers and crew, not to mention everyone along the flight path, unless the radiation is shielded by dense materials like lead. The mass of the shielding and the weight of the power conversion machinery of a fission reactor essentially negate the energy density argument for aircraft (ships and submarines are a different matter, since they can use displacement to carry the mass of the reactor). We can see a bit of this in regular aviation history. Helicopters were delicate, expensive and difficult to fly because the piston engines were heavy and offered very little power to overcome the weight and drag of the helicopter. Only when gas turbines became common did helicopters really take off (heh), since the turbines offered a compact, lightweight power source for the helicopter. Helicopters were actually invented in the late 1920's early 1930's, and a few were actually in service in WWII (for example the Focke-Achgelis Fa 223 "Drache"), but there was no German "Air Cavalry" because these machines were underpowered. The turbine powered UH-1 "Huey" was a much different proposition...
But your coleopter can still use nuclear energy, just indirectly. The vehicle needs to have a microwave receiver (rectenna) built into the fuselage, and the city have powerful microwave emitters beaming energy to receptive coleopters as they fly. Safe corridors for flight include keeping people away from the beam path, and ensuring buildings and structures are not placed in such a way that they randomly scatter microwaves. The pilot may have to engage battery power to take off and climb into the beam path (and the batteries better be charged when it is time to land!), but electric aircraft powered by microwave beams have been demonstrated experimentally (for example, the Stationary High-Altitude Relay Platform), so this isn't theoretical.