Add custom element ID depending where the widget place is, sidebar or footer

Solved it by following the advice from @mmm. Using $args["id"] did the trick.

Using $args["id"] will return the following:

post-sidebar

footer-first

With a little change, my final code is:

public function widget( $args, $instance ) {
  extract($args);

  // ...

  <div id='instafeed-<?php echo explode("-", $args["id"])[0] ;?>' class="c-widget-instagram"></div>

  <?php

  echo $after_widget;
}

The result is:

<div id='instafeed-post' class="c-widget-instagram"></div>
<div id='instafeed-footer' class="c-widget-instagram"></div>

Thanks