It is always 'save_post' (or 'wp_insert_post' immediately after this). In $_POST['tax_input'] you will find all the terms for all taxonomies associated with the current post.
Example:
'tax_input' =>
array (
'location' =>
array (
0 => '0',
),
),
To change the terms you have to call wp_set_post_terms( $post_ID, $tags, $taxonomy ); manually, just changing these values will not work because they are set when the actions fire.
For an existing post that is updated you can hook into 'edit_post' and 'post_updated'.
Parameters for all these actions are $post_ID, $post in this order. For 'post_updated' there is a small change: $post_ID, $post_after, $post_before.