@moss just a random opinion -

ones i've seen recently with what you're asking for are "Return of Godzilla (1984)" which really has some of-the-era nuclear feels. also a lot of 80s Japan - journalists, hospital rooms, weird science, military and government scenes. a great suit with close up cybernetic head shots.

then "Shin Godzilla" which is more modern with a few evolutions of Gojira to draw from, kinda creepy and intense, very much a social satire of Japanese bureaucracy