I upvoted Nepe's answer and you should, too.
But let's look at some statistics...
Source: Radiation Emergency Medical Management
I couldn't quickly find a chart for megaton weapons, so let's take the chart at its word.
The moderate damage zone starts at a radius of 0.25 mile with a 0.1Kt device and doubles for every 10X increase in yield. The estimated moderate damage zone for a 1.2Mt device would be about 4.25 miles or 6.8 km.
The severe damage zone starts at a radius of about 0.15 mile and again doubles as the yield increases 10X for a target severe zone of about 2.5 miles or 4 km.
Just to give you an idea of what that means, cities as large as London have a radius of 25-30 miles (40-48 km). Denver, Colorado (USA), on the other hand, has an average radius of only 7 miles (11 km). My town has a radius of about 0.25 mile.
Thus, it really matters where the bomb falls.
Which is certainly true because crater size depends on what the ground is like. But ignoring that and using this handy-dandy calculator we discover that the B83 at maximum yield will produce a crater radius of 204.6 meters (671 feet) — meaning the crater at its deepest point is approximately 204.6 meters deep and that website says any structure within 1.25X of the radius will be severely damaged (255.75 meters or 838.75 feet).
Conclusions
The only way to survive a direct hit is to be a thousand feet (305 meters) below the surface. All important structures from administration to manufacturing would be that deep or deeper. The wealthy and people deemed key members of society would have their residences that deep. (As a side note, your society would likely use how deep a residence is as a measure of social status.)
Buildings outside the moderate damage zone will be what Nepe describes: low to the ground and made out of a lot of concrete and lead. No windows and sealed entrances. The idea is to let the shockwave wash over the top of the building with little or no edges or corners to trap fallout, allowing rain (when it comes again) to wash everything away from the building. In fact, the storm drain systems would be designed to trap and secure fallout.
If I recall correctly, as many as seven years are needed for most if not all fallout radiation to drop to safe(ish) levels. Thus, unlike that lovely drawing from the 50s, they'd have food, water, medical, and other supplies (like educational materials for children and a lot of reading/viewing material) stored for 7-10 years of adult consumption (children grow up) for each person in the facility regardless of age. Recycling would be advanced beyond what we see today as a matter of necessity. Even residences would have basic repair, manufacturing and fabrication facilities. I can't even imagine how much expanding foam would be kept on hand. Where the bomb exactly strikes is always unknown and the possibility of cracking the facility's shell is far from low. What this means is that sleeping and living accommodations would be the smallest part of these facilities, which along with manufacturing would have very large storage facilities as well as the means of conveniently refreshing supplies (elevators, conveyors, docks...).
I could easily imagine a very sophisticated water dispersal system... because you really can't trust Mother Nature to get around to cleaning up someone else's mess. The dispersal system would be used to wash away the fallout into the aforementioned storm drain system. Yes, dust storms would bring more fallout to bear, but that just means early warning systems and another good dousing.
Roads would be a bit wider than normal to more easily permit the passage of emergency vehicles. All facilities would have communication centers to allow for coordination of emergency services as well as coordination of the continuation of civilization. No, everybody won't be sitting in their bunkers waiting out the storm. There's work to be done and nukes this threatening would be born with little more stress than the common cold (OK, kinda... you see where I'm going).
Cities would be heavily distributed. The last thing anyone wants is dense population centers. Nobody would be allowed to live near critical manufacturing, research, and administration facilities. Those facilities would be spread apart. The goal is to be sure little to nothing is ever within the severe or moderate damage zones. This means your transportation system will be fast, efficient, and very likely underground. Subways (pretty deep ones...) would be the norm on the planet, and they'd have plenty of ways to re-route traffic. It also suggests that most distribution of goods is happening underground.
Finally... I'm not sure what would happen to agriculture. You really can't move that entirely (if at all practically) underground. Too many people to feed without the sun's energy. That means agriculture in a distributed society would be found everywhere with a ton of redundancy. This might mean the society is much more vegetarian than Earth is on average as cows and chickens are notoriously difficult to corral quickly. You'd have some underground to keep the species going... huh... agriculture on a regularly-hit-by-nukes world might need another question.
Why not just push the entire civilization underground? Because people go weird when they can't experience the sun and even in a non-solar-energy society the vast, vast, vast majority of the energy needed for any species to survive comes from the sun. Don't believe me? Try growing carrots in the dark. :-)
I'll mention one more thing: most worldbuilders don't consider the effects of economics in their worldbuilding. What I just described is incredibly expensive. It strongly suggests the best defense is a whomping good offense. This kind of pre-planned it-could-hit-anywhere-at-any-time societal response would have severe effects on the economy, likely leading to remarkable individual austerity. Keep in mind, just because you're willing to pay the price doesn't mean you can. I would therefore expect architecture to be practical, efficient, cost-effective, and fundamentally unadorned — but people (being people) would find a way to dress it up within their means. Still, I'd expect a residence on one continent to look just like a residence on another.
I can imagine the popularity of a radioactively-activated spray paint that would imbue concrete structures with amazing colors... proof that you can cast the proverbial vulgar hand gesture at your enemies.
OK, one more thing and then I'm through. I'm completely ignoring the effects of a nuclear winter, which in your scenario would be a big honking deal.