Do you think Junie and the man survived?

I would think they survived that blast, but most 1962 viewers would probably think they died.

The catch is that there could've been more bombs dropped if that was near a major target area as theorized by members of the crowd.

Seems unlikely they could have got to the cabin, grabbed up much canned goods and THEN finding the hidden entrance to the mine before the explosion, regardless of what the producers of the film want us to think.

Remember the old man Jake was the only one that knew where the mine was.

Even if the couple did make it there they'd have to live in that mine for years if this really was ground zero. They didn't have a geigercounter so they wouldn't know what the radiation levels were.

And even their water would be radiated and undrinkable even if it was in a spring (it had to come from the contaminated surface first)

It's pretty obvious they were the only ones who survived. There's no doubt that this trio was the most level headed. There was ample time to drive the truck to where he told them to, becuase there was time that elapsed while the five in the truck were sweating, as evidenced by the arrival of the mob who missed them.
Even in the sixties, the caverns and mines were thought by the more level headed ones to be safer than usual shelters. The spring would be less likely contanimated than water outside. Clearly, the grandpa sacrificed himself so there would be plenty of provisions for those two, and because the new world wouldn't be a picnic.


Lets not bicker about who killed whom

obviously they did survive to repopulate the earth, and we are their descendents.

It was believed in 1962 that radiation would dissipate to a safe level in about 14 days. Cobalt-based weapons weren't in use then, and they didn't have the abundance of nukes in 1962 that there were a few years later, so it was likely that the target in that area would only get one such nuke, or perhaps two in succession. The likely targets were the city (35 miles), a command headquarters (25 miles), and a missile refuel refinery (15 miles). The city would have targeted and probably the command headquarters. At 25+ miles away, they would have survived even a 1 megaton blast, although the air and thermal blasts may have damaged the truck. Whether they damaged the cabin depends on the location of the mountains.

Junie and Peter had about 5 minutes from the time they left in Jake's truck until the time the blast hit. They would have survived the initial blast. The radiation wouldn't arrive for at least another hour, giving them time to get to the cabin (walking if necessary) stocking up food and possibly bringing other supplied (i.e. mattresses, cots, sleeping bags), finding the mine (which was 100 yards from the cabin), and setting up a camp deep inside. The elements inside of the cave would filter whatever radiation existed and provide fresh air flow. Food would need to be rationed; water was provided by the underground spring.

The downside was the possibility that the shock of the blast would have collapsed parts of the mine, but this would have probably happened before they went inside. Other problems in the mine would be bats and mice or other living creatures. They also would have needed the sense to stock required things. I won't get into the aftermath when the radiation in the air sank to acceptable levels, as that's a long topic.