Output of a value at a given date and location in Google Earth Engine

I assumed your AOI is in Greenland and took an arbitrary point in that region. For range dates in your code, only 3 images in Image Collection were selected for that point. So, you can print a paired list of dates and albedos directly in Console of GEE code editor by using an ee.Reducer object. Full code looks as follows:

var pt = ee.Geometry.Point([-48.08513183593751, 66.870153741717]);

var albedo = function(image){
  var alb = image.expression(
  "((0.356*blue)+(0.130*red)+(0.373*nir)+(0.085*swir)+(0.072*swir2)- 0.018)/ 1.016",
  {
    'red': image.select('B3'),
    'blue':  image.select('B1'),
    'nir':  image.select('B4'),
    'swir':  image.select('B5'),
    'swir2':  image.select('B7')
  });
  return(image.addBands(alb.rename("albedo")));
};

var dataset = ee.ImageCollection("LANDSAT/LC08/C01/T1_TOA")
                  .filterDate('2020-06-01', '2020-06-30')
                  .filterBounds(pt)
                  .map(albedo);

print("dataset",dataset);

var myAlbedo = dataset.select("albedo"); 
print("myAlbedo",myAlbedo); 

var getAlbedo = function(image) {

  // Reducing region and getting value
  var value_albedo = ee.Image(image)
    .reduceRegion(ee.Reducer.first(), pt)
    .get('albedo');

  return value_albedo;
};

var count = myAlbedo.size();

var albedo_list = myAlbedo.toList(count).map(getAlbedo);

print("albedo list", albedo_list);

var img = myAlbedo.first();

Map.addLayer(img);
Map.addLayer(pt);

var allDates = myAlbedo.aggregate_array('system:time_start');

var allDatesSimple = allDates.map(function procDates (ele) {
  
  return ee.Date(ele).format().slice(0,10);
  
});

var paired = allDatesSimple.zip(albedo_list);

print (paired);

After running above code in GEE code editor, I got result of following image. In console you can observe the paired list of dates and albedos for that point.