I watched that (B&W) nuclear movie in 1988 on TV. Post-apocalyptic family survivors of a nuclear attack are grouped together for days in the basement of their house, where fear and dwindling supplies wear away at their dynamic. After days waiting for radiation level comes down the man gets out basement and he see many dead bodies on the streets. The man starts a journey to find a unique place on Earth where is free of nuke radiation.
On the journey a woman follows him but he does't want her near him because gangs could kill them. At the end he found a ship in which there is food for fifty years but nobody gets into and neither who is inside the ship gets out. Finally, he gets to climb on board the ship and escaped swimming to the beach where that woman was waiting for him. That is the only color scene of the movie at the END on the beach with the woman.