Here is another good (in a depressing sort of way) from way back in 1959. I couldn't find a decent trailer for it so this will have to do.
https://en.wikipedia.org/wiki/On_the_Beach_(1959_film)
No happy endings in this one either.
This one and "The World, the Flesh and the Devil" (also 1959) were probably the first serious big budgeted movies about nuclear war (nuclear bombs weren't the cause in "The World, The Flesh and the Devil" but the cause was the not clearly defined weaponized use of "nuclear isotopes").