If I’m understanding you correctly get_term_children does what you want.
$term_id = 2;
$tax_name="locations";
$term_child = get_term_children( $term_id, $tax_name );
Another possibility would be using get_categories, it has an child_of, taxonomy and depth parameter – the documentation on wp_list_categories, which offers pretty much the same functionality, is better.
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