How to run function for each element on arrays

It appears that the double loop going through the coordinates does not wait for the response from the ajax (I'm assuming that all of the coordinates are required before processing). Since the ajax call is asynchronous, the locations won't be populated until the server responds; however, the loop going through the locations array will start executing immediately after the initial request is made to the server and, most importantly, before the locations are populated.

Try moving a majority of your function into the success function.

function showPosition(position){

  let locationLatitude = []
  let locationsLongitude = []

  //AJAX CALL TO GET THE POSITION OF THE PLACES AND PUSHING THEM TO THE ARRAYS
  let success = function(res){
    let locations = res.locations

    for (var i=0; i<locations.length; i++){
      locationLatitude.push(locations[i]['place_latitude'])
      locationsLongitude.push(locations[i]['place_longitude'])
    }

    // LOOP TO GET ALL COORDIANTES FROM PLACES (LAT,LONG)
    var locationLatitudeLength = locationLatitude.length
    var locationsLongitudeLength = locationsLongitude.length
    let startPosLat
    let startPosLong

    for(var i=0; i<locationLatitudeLength; i++){

      for(var j=0; j<locationsLongitudeLength; j++){
        startPosLat = locationLatitude[i]
        startPosLong = locationsLongitude[j]

        userlocationLatitude = position.coords.latitude
        userlocationLongitude = position.coords.longitude

        //PASS VALUES OF COORDINATES TO THE FUNCTION
        let distance = calculateDistance(startPosLat, startPosLong, userlocationLatitude, userlocationLongitude)
      }
    }

    if(distance < .05){
        $('.div-image').attr('src', 'pic2.jpg')
    }else if(distance > .05){
        $('.div-image').attr('src', 'pic.jpg')
    }
  }

   $.ajax({
      type: 'GET',
      url: '/api/locations',
      crossDomain: true,
      dataType: 'json',
      async: false,
      success : success,
  });

  //function to calculate the distance between two points of coordinates 
  function calculateDistance(lat1, lon1, lat2, lon2) {
      var R = 6371; // km
      var dLat = (lat2-lat1).toRad();
      var dLon = (lon2-lon1).toRad();
      var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
              Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) *
              Math.sin(dLon/2) * Math.sin(dLon/2);
      var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
      var d = R * c;
      return d;
  }

  Number.prototype.toRad = function() {
    return this * Math.PI / 180;
  }
}```

I would first suggest using an array of arrays to store coordinates so your latitude and longitude are referenced near eachother. I have given some basic examples of looping, assuming checkFunction is something you define to handle the coordinate checks.

You can use vanilla JS to loop like this:

for (var i in myArray) {
   checkFunction(myArray[i]);
}

Or you can use JQuery to loop like this:

$(myArray).each(function(index, value) {
    checkFunction(value);
});