"The Moon is Green" by Fritz Leiber. It follows Effie, a house-wife who likes to stare up at the moon, which is green due to the fallout and radioactive dust. There's a recurring theme of the community constantly scanning themselves with geiger counters to prove that they're not contaminated. The man who comes to the window claims that the radiation has birthed new wonders:
Effie, desperate for news of the outside world, asks what it’s like, and Patrick (who already seems rather reminiscent of a fairy traveler) tells her that while the radioactive dust did at first bring about only death and ugliness, life soon adapted into a veritable fairyland “more amazing than you tombed folk could ever imagine.” Patrick’s description of this wonderland, replete with giant stingless bees and rainbow serpents and wonderful, dark-skinned children with 14 fingers and 16 toes who move about faster than the eye can see
It turns out that Patrick is simply immune to the radiation, but she leaves with him anyhow, and it seems she may also be immune.
Hank scans Patrick with his Geiger counter, “the Twentieth Century’s mouthpiece of ultimate truth”, and gets him to admit he had made the whole thing up – what’s outside is, he admit, just a little bit worse than either of them could imagine. Patrick himself is somehow resistant to radiation, a modern-day “Rappaccini’s child” who wanders the world alone.
Effie, enraged by this further killing of beauty piled on top of that regularly inflicted by Hank, declares that she can’t and won’t be cooped up any longer and is leaving for the garden. The two men watch her disappear into the greenish murk of the surrounding cityscape, at which point Patrick declares that he’s going after her, given that she also seems strangely resistant to the dust. Hank seals them both out and stays behind scanning himself with the Geiger counter.
As per user14111's comment, it's "Available as a Project Gutenberg etext or in the Internet Archive scan of the April 1952 Galaxy or the X Minus One radio adaptation"