В качестве интересного мыслительного упражнения я придумал следующее:
SELECT a.areas_name,
a.areas_id,
n.neighborhoods_id,
n.neighborhoods_name,
n.neighborhoods_area_id,
a.areas_state_id
FROM neighborhoods_db AS n
INNER JOIN areas_db AS a ON a.areas_id = n.neighborhoods_area_id
WHERE a.areas_state_id = $mxstateid
AND n.neighborhoods_id in (SELECT restaurants_neighborhood FROM restaurants_db)
ORDER BY a.areas_id, n.neighborhoods_name ASC
Кроме того, псевдонимы таблиц - ваш друг.