The safest place to be on Earth during a nuclear war lies outside the range of nuclear fallout, or in a suitable shelter which protects you from it. Building a suitable fallout shelter is neither totally protective from radiation, nor cost effective, but I've provided more details about shelters below. First, I'll give a description of nuclear fallout.
Nuclear fallout is a dusty, hazardous, radioactive material which carries through, and rains down from the planet's atmosphere following the event of a nuclear explosion. Since nuclear fallout can disperse through the atmosphere in a variety of ways, a more practical answer to the initial question of safest locations lies somewhere outside the range of our planet's atmospheric conditions.
We don't have many resources in outer space that we've located, required for our survival, such as food and water, so this gives you an even more practical answer. There is nowhere safe to be on Earth during the event of a large scale nuclear conflict.
Perhaps somewhere underground would have some benefits and be a suitable alternative, but one has to consider that nuclear radiation penetrates through objects. You need a shelter encased entirely within objects which have radiation blocking properties such as lead, concrete, or packed dirt in appropriate thicknesses.
We're talking concrete three feet thick, and even more is better. Doing a simple Google search on the Internet will reveal many sites which have information related to constructing nuclear fallout shelters. All of the information needed to do this is readily available from a diverse variety of sources.
Keep in mind though, in many places, including the State of Michigan where I'm from, there are laws against tunneling through the ground such as in the movie "Blast From The Past." So, constructing a feasible nuclear fallout shelter would probably anger the government and cause them to raid your property and destroy your work in progress. Not to mention, a fallout shelter like that is probably not feasible in the first place, but also perhaps necessary to completely avoid exposure to radiation.
If you worked for the government and had special clearance and availability to NASA's shuttle factories, you could replicate one of their shuttles and load it with massive amounts of food. Probably the only other option is to stay here like everyone else and suffer the consequences of military technology and sadistic egos conflicting after years of mounting turbulence.
That's sort of a dreary answer, but it's probably the most realistic one I've seen. Once the nukes start going off, the contamination of nuclear poisoning is not going to be a localized thing. A large scale nuclear war would likely spread radioactive material over the entire earth in varying amounts.