MySQL - Exclude a result if even one foreign key doesn't meet criteria (date availability checker)
You need a DISTINCT because of the n:m relationships
But the date selection i would write differently, so that all holtel.id should be excluded, which have a reservation on that day, so that it can't be choosen anymore
Schema (MySQL v5.7)
CREATE TABLE `reservations` (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `hotel_id` int(10) unsigned DEFAULT NULL,
  `start_date` date DEFAULT NULL,
  `end_date` date DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=3 DEFAULT CHARSET=utf8;


insert  into `reservations`(`id`,`hotel_id`,`start_date`,`end_date`) values
    (1,1,'2020-08-26','2020-09-02'),
    (2,1,'2020-12-06','2020-12-13');


CREATE TABLE `regions` (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `region_name` varchar(255) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=6 DEFAULT CHARSET=utf8;

insert  into `regions`(`id`,`region_name`) values
    (1,'Region 1'),
    (2,'Region 2'),
    (3,'Region 3'),
    (4,'Region 4'),
    (5,'Region 5');


CREATE TABLE `hotels` (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `region_id` int(10) unsigned DEFAULT NULL,
  `hotel_name` varchar(255) DEFAULT NULL,

  PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=6 DEFAULT CHARSET=utf8;

insert  into `hotels`(`id`,`region_id`,`hotel_name`) values
    (1,1,'Hotel 1'),
    (2,3,'Hotel 2'),
    (3,5,'Hotel 3'),
    (4,5,'Hotel 4'),
    (5,4,'Hotel 5');


Query #1
SELECT 
    DISTINCT hotels.hotel_name, regions.region_name
FROM
    hotels
        LEFT JOIN
    reservations ON hotels.id = reservations.hotel_id
        LEFT JOIN
    regions ON hotels.region_id = regions.id
WHERE
(reservations.start_date is NULL OR reservations.end_date is NULL)

        OR hotels.id NOT IN
        (SELECT h.id 
FROM hotels h
    INNER JOIN 
    reservations r ON h.id = r.hotel_id
WHERE
   CAST('2020-09-02' AS DATE) BETWEEN r.start_date AND r.end_date)  
;





hotel_name
region_name




Hotel 2
Region 3


Hotel 3
Region 5


Hotel 4
Region 5


Hotel 5
Region 4




View on DB Fiddle