It's likely that you're referring to a specific region or group of languages that were least influenced by Indo-European migrations.
To answer your question properly, I need more information about the specific region or language family you are referring to. Please provide the following:
* The specific region or language family you're interested in: For example, are you asking about languages spoken in the Basque Country, the Caucasus, or the Americas?
* What you mean by "least influenced": Are you asking about languages that retained the most original features, or those that adopted the fewest Indo-European loanwords?
Once I have this information, I can give you a more accurate and helpful answer about how Indo-European migrations affected the languages of that region.