Question: It's 2016, but for some reason, the Cold War never ended. You've been inspired by your (for some inexplicable reason) favorite movie, Indiana Jones 4, to start a new business: building refrigerators. However, the market is so saturated that in order to distinguish yourself with a nice marketing campaign, you decide to make them **NUKEPROOF!** 

The refrigerator should be:

1. Usable as a real refrigerator would be.
2. No bigger than standard double door refrigerator, so no room-sized walk-in refrigerator. Though, you *can* add some additional size for additional armor, for example, in **reasonable** margins, so nothing like 10 meters of iron from one side.
3. Protect one person from up to 1.2 megatonnes of a TNT nuke at a minimum distance of 2 km from the explosion.

How are you going to design it and what materials are you going to use?

Answer: 
GrinningX has quite a good answer but I would like to amend it slightly. The stats quoted appear to refer to a ground burst. Ground bursts are not thought to be targeted against cities because air bursts are more damaging to them. Ground bursts are expected to be used against hardened targets like ICBM silos. 

However, if a 1.2MT ground burst did occur in your city it the fridge owner would die for sure. Ground bursts generate enormous quantities of fallout. (Air bursts generate almost no fallout.) Fallout is created when energetic neutrons in the fireball touch heavy matter, converting it into unstable isotopes. Air burst neutrons interact with gasses, and the radioactive isotopes they make from this gas tends to stay aloft. 

The fallout from such a ground burst would be lethal for weeks to months - far too long to be hiding inside a refrigerator. 

On the other hand, an air burst produces almost no radiation on the ground (neither prompt nor fallout) so the radiation shielding would be largely unneeded. The most important need would be (in this following order of events) 1) protection from the flash (just being inside your house and away from windows is probably good enough), 2) protection from blast (sturdy steel construction and being securely bolted to a sturdy foundation would keep you alive), 3) protection from the heat and fumes from your house burning down, and 4) a mechanism to allow you to exit the fridge even though it has been buried by the debris of your house. Numbers 3 and 4 are quite a bit more difficult and complicated than 1 and 2. 

For surviving the fire, maybe some kind of hand-cranked air pump which pulled air in from outside and percolated it through a container of water (to cool the air and remove smoke)? That would help, but would not do anything to reduce carbon monoxide or lethal carbon dioxide levels. Heat would be less of a problem. Fridges are designed to be insulated, so just make sure the gaskets are fire resistant and increase the R value enough to survive. 

I'm honestly not sure how to handle egress. It's hard to guess what debris will be on the fridge and how it will be shaped. I don't have any good ideas for this one.
Your customers will need to:
Put your fridge underground in the cellar;  

Reinforce the cellar walls to withstand the shockwave of the blast and the collapse of the house on top. 

Add shielding in 2 layers, preferably tungsten, 0.5" each layer, since lead is just messy, on the outer side of the body, and on the inside, just behind the fibreglass interior. Put the insulation in between the two layers of tungsten. The piping and wiring to the outside from the inner compartment should leave through the bottom of the fridge.  

Recommend buyers get **TWO** fridges, or one for every member of the family and a spare for actually keeping food in.