I am not sure whether underground bunkers will be immune from radiation. But even if they are safe, I am afraid that only a very small number of individuals could be housed in such facilities for long-term.
There are some speculations that there are some compounds underground , maybe whole city. But when you think about it , its not imposible to build whole city underground. It only requiers a lot of money to invest, but its possible .
There are many underground bases in Russia, for example:
https://en.wikipedia.org/wiki/Mount_Yamantau
Large excavation projects have been observed by U.S. satellite imagery as recently as the late 1990s, during the time of Boris Yeltsin's government after the fall of the Soviet Union.[1] Two garrisons, Beloretsk-15 and Beloretsk-16, were built on top of the facility, and possibly a third, Alkino-2, as well, and became the closed town of Mezhgorye in 1995. They are said to house 30,000 workers each. Repeated U.S. questions have yielded several different responses from the Russian government regarding Mount Yamantaw.[2] They have said it is a mining site, a repository for Russian treasures, a food storage area, and a bunker for leaders in case of nuclear war.[3] Responding to questions regarding Yamantaw in 1996, Russia's Defense Ministry stated: "The practice does not exist in the Defense Ministry of Russia of informing foreign mass media about facilities, whatever they are, that are under construction in the interests of strengthening the security of Russia."[3] Large rail lines serve the facility.[3]