<OK, my time to shine
Let's take Tsar bomba then. Yield of 50Mt(TNT). So they say.
Interestingly enough, 50Mt(TNT) also happens to be best estimate of yield of Hunga Tonga volcanic explosion earlier this year. Though in this case, almost all the energy was released as a shockwave, rather than just a good half of it. So, let's compare the two.
https://www.volcanocafe.org/hunga-tonga-and-the-supercriticality-event/ (source for 50Mt figure)
The explosion of Hunga Tonga, as you probably know, was so fuckhuge that it was heard all the way to Anchorage, Alaska. That's a distance of some 9350km.
https://twitter.com/NWSAlaska/status/1482431322740060162
Now Tsar bomba was heard 780km away at Dikson Island, where it's reported that a glass also shattered (but that seems to be more a fluke, as we'll see soon.) Nobody heard it in more nearby Amderma, though, but perhaps just nobody was paying attention.
Either way, Hunga Tonga was VERY audible in Fiji (huge boom) at 700km and quite audible in New Zealand at 2000km. So, yeah. Apparently the shockwave from Hunga Tonga was more intense, sharper than that of Tsar bomba. We will use this to argue that destruction from Hunga Tonga can only serve as upper limit for estimation of nuclear explosion (and realistically we would be looking at quite a bit smaller effect).
Again, Tsar Bomba's shockwave circled Earth three times, and was measured as 0.6mbar the first time in Wellington, New Zealand. Hunga Tonga's shockwave circled Earth "for days" and was measured as 2.5mbar in Switzerland and 2mbar in England. And yet, in the capital of Tonga, Nuku'alofa, 65km away, it does not seem to have shattered much glass, judging by photos: https://upload.wikimedia.org/wikipedia/commons/6/65/NZDF_Saint_George%27s_Palace_January_2022.jpg
Tsar bomba is massively overdimensioned. Typical warheads are in the range of a couple hundred kt(TNT). Yes, some missiles can carry multiple warheads, but we're looking at a Mt or two max.
At this point, let me mention that shockwave effects geometrically scale with square of distance (at least, if we ignore dissipation, or possible effects of acoustic focusing by objects/landscape). This is simply a consequence of same amount of energy having to reach a sphere whose surface area grows with square of radius. (Well, once we're dealing with long distances, longer than height of the atmosphere, this becomes a linear law instead, as height is no longer a possible direction of shockwave spreading. It just terminates.) So a 500kt(TNT) bomb, with 100x smaller yield than Tsar bomba, will have similar effects on 10x smaller distances. Little Boy and Fat Man, with their 15-20kt(TNT), again have similar effect on yet 5-6x smaller distance (square root of ratio between 15-20 and 500).
Let's then look at reports of damage in Hiroshima and Nagasaki to get a sense of scale.
http://www.nasonline.org/about-nas/history/archives/collections/organized-collections/atomic-bomb-casualty-commission-series/abccrpt_pt3app9ch3.pdf
In Hiroshima, wooden houses (pretty much all the structures in Japanese cities at the time) were pulverized up to 1-2km, destroyed up to 2-3km, badly damaged up to 3-4km and unlivable but still standing. But for concrete buildings, outside 1km there was almost no damage observed. So, if your city is not build of cardboard, this is the metric you should be looking at.
In Nagasaki, damage is greater, not so much due to slightly higher yield than due to topography.
Cross-checking with nukemap you mentioned: for 15kt Little Boy, it says:
>Heavy blast damage radius (20 psi): 340 m (0.36 km²)
>Moderate blast damage radius (5 psi): 1.67 km (8.78 km²)
>Light blast damage radius (1 psi): 4.52 km (64.1 km²)
So, you should take the first metric as radius within which even concrete buildings are destroyed, second metric as radius within which wooden buildings are destroyed (but at this radius, concrete buildings are practically unscathed, aside for windows and doors getting rekt), and the third metric as radius within which even wooden buildings survive (but again, windows might get rekt).
Scaling this up 6 times, we get:
>Heavy blast damage radius (20 psi): 2.04 km
>Moderate blast damage radius (5 psi): 10.02 km
>Light blast damage radius (1 psi): 27.12 km
But that's without accounting for dissipation, airburst, etc.; for 500kt nukemap instead gives:
>Heavy blast damage radius (20 psi): 1.73 km (9.37 km²)
>Moderate blast damage radius (5 psi): 3.63 km (41.5 km²)
>Light blast damage radius (1 psi): 9.34 km (274 km²)
And for 50Mt Tsar bomba:
>Heavy blast damage radius (20 psi): 8.91 km (249 km²)
>Moderate blast damage radius (5 psi): 20.7 km (1,350 km²)
>Light blast damage radius (1 psi): 54.3 km (9,270 km²)
Given that not even windows were really rekt in Nuku'alofa from Hunga Tonga explosion, 65km away, I would say the "Light blast damage radius" of 50km for Tsar bomba is perhaps slightly exaggerated. And the descriptions of damage are not necessarily wrong, but they're vague on the side of sensationalisation. But I concur.
Now, regarding radiation... there's a big difference between being outside and inside. Why? Because most of the radiation release is blocked by structures. Thermal radiation which is the cause of burns is blocked by solid walls instantly, so just duck and avoid being irradiated through the window. And concrete is also fairly good shield from gamma rays; not as good as lead but still, 15-20% per cm (depends on wavelength.) Similar values for most comparable materials. So your typical 30cm exterior wall will block but a couple ‰ of ionising radiation. So, stay inside and you're good. Even better if you can go further inside so you're also shielded by another interior wall.
Now, let'sgo back to the report from Japan, we can read further down reports of people who survived by being in concrete buildings, closer than 1km to the centre:
>Nippon Bank ... 0.4km south-east ... Out of the total of 75 members, victims were counted as 43.
(in Hiroshima) and several more concrete buildings listed in both cities. As a curiosity, in Nagasaki:
>50 persons were working to arrange sewage in a cave trench of a hill beside the Nagasaki Prison, just under the explosion center. 7 persons among them, who were in a deepest corner, survived.
So, that's basically survivors directly in ground zero, simply by the sheer luck of being a bit underground, not even in a real bunker.
In light of this, it should also not be surprising that Jesuit priests survived the Hiroshima bombing because they were inside the church at the time, something passed around as a "miracle" by ignorants.
6km² ≠ 6km x 6km. 6km² is a circle of radius 1.38km. Superimposed to Moscow, that's about the size of inner ring road on your map.
tl;dr nuclearsecrecy.com / nukemap is a psyop that perpetuates the cold war era myth of nukes as the ultimate apocalyptic weapons, cultivated to enforce sword of damocles psychology and to enforce status quo through threat of mutually assured (fictional) destruction. Just stay inside bro. And avoid windows.