The best place to search for a location for a Lifehaven would be in the Southern Hemisphere coupled with an island, and with some large existing caves. The search begins with a Google search, a Wikipedia search, a Flickr search, YouTube search and a Google Earth look at the discovered sites.
Easter Island has a few small natural caves formed from lava tubes but nothing that would serve as a Lifehaven without essentially constructing the interior volume from scratch.
Tasmania has many caves and some of them may be useful with little preparation to the volume, but they do seem to be filled with water. Water may not be a bad thing if it is coming from the deeps, and not from the surface. Here is a map of the cave areas.
Fiji didn’t mention anything about caves.
New Zealand has a List of Caves on the Wikipedia.
Somoa has few caves.
The Cook Islands has burial caves which appear to be lava tubes.
Antarctica has ice caves which would not necessarily be impossible to convert to Lifehavens, but because the ice functions as a fluid the caves would have to support the weight, and pressure, and would essentially be submarines. There may be caves on the Palmer Peninsula but I didn’t find any on Google.
Flickr Hive Mind caves (tags)
Borneo has caves a plenty because of its limestone, and rain. The Gunung Buda Project is exploring some of the biggest caves in the world. This island lays abreast of the equator, and in the middle of a questionable area politically. However these large caves could have apartment houses constructed in them immediately.
United States has some big caves such as Mammoth Cave, and Kentucky, Carlsbad Caverns, New Mexico. These would be okay but they are in the Northern hemisphere. Under Detroit Michigan, there are large (1,400 acres, about 2 square miles of floor space) of salt mines with good potential for Lifehavens. At the moment they are not being worked, but no matter there is plenty of space. Detroit Salt Mine tour. Other salt mines around the world might be good also. One problem with the Detroit Salt Mine is that it is a target being next to a Ford Motor Company plant, and on a choke point for the Great Lakes shipping.
Mexico has some caves.
This search didn’t find any caves like which were in the preferred description, and it may be necessary to construct the Lifehaven out of living rock. This may not be difficult using modern mining techniques.
There already exists many seed banks, but the one most likely to survive a major disaster, other than war, is this one.
It is located at Longyearbyen (78.239N 15.495E) which is very remotely located near the north pole, but for the purposes of a human Lifehaven it is in the wrong hemisphere for surviving an atomic war. It has the additional severe disadvantage of being located very near an airport that is certainly a target during a major war because it is the only airport on a direct path between the super powers. Also, it is in the Gulf Stream and is above freezing temperature three months per year.