What is the pun in this sentence you have thus surveyed country on every side within a dozen miles of where live?

The pun is in the phrase "surveyed country". It plays on the double meaning of "survey" which can mean:

* To examine or inspect an area of land: This is the literal meaning used in the sentence.

* To ask people questions in order to find out their opinions or experiences: This meaning suggests the person has been asking around about the local area.

The sentence implies the person has explored the land itself, but also might have been gathering information from the locals.