You are going to have to JOIN twice on the postmeta table. Something like:
SELECT $wpdb->posts.ID, $wpdb->posts.post_title, $wpdb->terms.name, wpcflat.meta_value AS latitude, wpcflong.meta_value AS longitude
FROM $wpdb->posts
/* First Join */
LEFT JOIN $wpdb->postmeta as wpcflong ON $wpdb->posts.ID = wpcflong.post_id
/* Second Join */
LEFT JOIN $wpdb->postmeta as wpcflat ON $wpdb->posts.ID = wpcflat.post_id
LEFT JOIN $wpdb->term_relationships ON($wpdb->posts.ID = $wpdb->term_relationships.object_id)
LEFT JOIN $wpdb->term_taxonomy ON($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id)
LEFT JOIN $wpdb->terms ON ($wpdb->term_taxonomy.term_id = $wpdb->terms.term_id)
WHERE 1
/* Meta queries for lat and long */
AND wpcflat.meta_key = 'wpcf-latitude'
AND wpcflong.meta_key = 'wpcf-longitude'
/* I don't know what criteria you are using to calculate 'nearest'
but you'd need more conditions here for that */
AND $wpdb->posts.post_status="publish"
AND $wpdb->posts.post_type="places"
AND $wpdb->term_taxonomy.taxonomy = 'countries'
As noted in my SQL comments, I don’t know what you are using as criteria for ‘closest’ but that code will get you both meta values to play with. My database doesn’t have lat and long data so I can’t test that strictly speaking but it is correct in principle, barring a typo or two or other stupid mistake.
Subqueries are another possible solution but they do not perform well when you try to sort or filter on them.