Mysql. Order locations and join listings randomly

I have two tables: locations and listings.

locations
id title address latitude longitude

listings
id location info status

SELECT locations.title, 
       locations.address, 
       ( 3959 * acos( cos( radians('".$center_lat."') ) * cos( radians( latitude ) ) * cos( radians( longitude ) - radians('".$center_lng."') ) + sin( radians('".$center_lat."') ) * sin( radians( latitude ) ) ) ) AS distance      
  FROM locations 
ORDER BY distance

This will list the locations in order by location with the users provided latitude and longitude. Works perfect, but what I really want to do is..

List one "listings" per location, and have the locations remain in order.
If a location has more then one "listings" have it be completely random.

Would it be better to do this all in one SQL query? Or populate all the locations that have atleast one "listings", then use another query to select a random "listings" for that location?

UPDATE

Provided create table:

CREATE TABLE `listings` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `token` varchar(4) DEFAULT NULL,
  `location` varchar(45) DEFAULT NULL,
  `info` varchar(45) DEFAULT NULL,
  `status` varchar(45) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=MyISAM AUTO_INCREMENT=24 DEFAULT CHARSET=utf8;

CREATE TABLE `locations` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `title` varchar(45) DEFAULT NULL,
  `address_street` varchar(45) DEFAULT NULL,
  `addrees_city` varchar(45) DEFAULT NULL,
  `address_state` varchar(45) DEFAULT NULL,
  `address_zip` varchar(45) DEFAULT NULL,
  `latitude` decimal(10,6) DEFAULT NULL,
  `longitude` decimal(10,6) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=MyISAM AUTO_INCREMENT=6 DEFAULT CHARSET=utf8;

To output the locations.title if the location has at least 1 row associated with it in the "listings" table, use:

SELECT loc.title
  FROM LOCATIONS loc
 WHERE EXISTS(SELECT NULL
                FROM LISTING li
               WHERE li.location = loc.id)

Use:

  SELECT x.title, 
         x.address,
         x.distance,
         x.info,
         x.status
    FROM (SELECT loc.title, 
                 loc.address, 
                 ( 3959 * acos( cos( radians('".$center_lat."') ) * cos( radians( latitude ) ) * cos( radians( longitude ) - radians('".$center_lng."') ) + sin( radians('".$center_lat."') ) * sin( radians( latitude ) ) ) ) AS distance,
                 li.*,
                 CASE 
                   WHEN @location = loc.id THEN @rownum := @rownum + 1
                   ELSE @rownum := 1
                 END AS rank,
                 @location := loc.id
            FROM LOCATIONS loc
       LEFT JOIN LISTINGS li ON li.location = loc.id
            JOIN (SELECT @rownum := 0, @location := -1) r
        ORDER BY loc.id, RAND()) x
   WHERE x.rank = 1
ORDER BY x.distance

Using MySQL 5.1.49-community, I've successfully rendered the desired results with the query above.

I'm unable to reproduce the OP's duplicated row using:

CREATE TABLES

CREATE TABLE `locations` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `title` varchar(45) DEFAULT NULL,
  `address_street` varchar(45) DEFAULT NULL,
  `address_city` varchar(45) DEFAULT NULL,
  `address_state` varchar(45) DEFAULT NULL,
  `address_zip` varchar(45) DEFAULT NULL,
  `latitude` decimal(10,6) DEFAULT NULL,
  `longitude` decimal(10,6) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=6 DEFAULT CHARSET=latin1$$

CREATE TABLE `listings` (
  `id` int(11) NOT NULL,
  `token` varchar(4) DEFAULT NULL,
  `location` varchar(45) DEFAULT NULL,
  `info` varchar(45) DEFAULT NULL,
  `status` varchar(45) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1$$

INSERT statements:

INSERT INTO `locations` 
VALUES (1,'John\'s Ice Cream','1701 S Martin Luther King Jr Blvd','Lansing','MI','48910','42.714672','-84.567139'),
       (2,'7 Eleven','3500 Okemos Rd','Okemos','MI','48864','42.683331','-84.431709'),
       (3,'Kurt\'s Pizza','213 Ann St.','East Lansing','MI','48823','42.736053','-84.481636'),
       (4,'Walmart','16275 National Pkwy','Lansing','MI','48906','42.780350','-84.637238'),
       (5,'Alex\'s Hot dog Shop','8505 Delta Market Dr','Lansing','MI','48917','42.739830','-84.677330');

INSERT INTO `listings` 
VALUES (19,'39c4','1','5 gallons for $8','active'),
       (21,'89dF','4','2 mens shirts for $2','active'),
       (22,'67oP','1','Ice cream cones for $1','active'),
       (23,'5tG8','2','Large soft drinks only $0.99!','active');