The following examples are admittedly overly-simplified in terms of which category they are placed in.
a thought exercise in part because the (fractured) USA won't have been the only survivor - and probably isn't the only (sub)nation fighting the Overlords.
First would be the countries whose geology afforded a great many places to hide, preferably underground. Example: Afghanistan.
Then the countries where a combination of history and geology have created passageways and hiding holes. Examples: Switzerland, Peru, Wales.
Then the countries where human history has carved hiding places underground. Examples: United States of America, Russia. (thank you, Cold War)
...and thinking about the Cold War's underground refuges, led to thinking about the other direction during that time. And thus was born The High Ground, now at LJ & AO3.