Get Thumbnails and Thumbnails URL from Media Manager

I assume you need to show the image url to the user, for all sizes, within the Attachment Details screen.

Using Underscore/Backbone

We can extend the Attachment Details View, in a similar fashion as in my previous answer here and based on the media views in the core:

<!-- Custom template part -->
<script type="text/html" id="tmpl-wpse-url-per-size">
    <div class="wpse-url-per-size" style="padding-top:5px; clear:both;">
        <h2>Show URL Per Image Size</h2>
        <label class="setting">
            <span>Size</span>
            <select id="wpse-select">
                <option value="">Select</option>
                <# _.each( data.sizes, function ( item, size) { #>
                    <option value="{{item.url}}">{{size}} {{item.width}}x{{item.height}} 
                <# } ) #>
            </select>
        </label>
        <label class="setting">
            <span>URL</span>
            <input type="text" id="wpse-url" readonly>
        </label>
        </div>
    </div>
</script>

and

<!-- Extend the Attachment Details View -->
<script>
jQuery(document).ready( function($) 
{   
    var m = wp.media;       

    m.view.Settings.AttachmentDisplay = m.view.Settings.AttachmentDisplay.extend(
    {
        template: function(view){
            return m.template('attachment-display-settings')(view)
            + m.template('wpse-url-per-size')(
                {sizes: this.options.attachment.get('sizes')}
            );
        },
        events: _.defaults( 
            m.view.Settings.AttachmentDisplay.prototype.events, 
            { 'change #wpse-select': 'wpse_change' }
        ),
        wpse_change: function(e){
            this.$( "#wpse-url" ).val( this.$('#wpse-select').val() );
        }       
    } );
} );
</script>

This is then hooked into the print_media_templates action.

Here we don’t need to override the render() method, as done here by @kalimah-apps, since we override the events() method instead.

The available image sizes can be filtered through the image_size_names_choose filter, where the default ones are thumbnail, medium, large and full.

Here’s an example:

Using the attachment_fields_to_edit filter

We can e.g. create a custom form field with a select box and a readonly input text, via the attachment_fields_to_edit filter, to display the image url for each image size:

Here’s a demo plugin:

<?php
/**
 * Plugin Name: Show Image URL For All Image Sizes
 * Description: Show the image url,  for all image sizes, under the 'Attachment Details'
 * Plugin URI:  https://wordpress.stackexchange.com/a/232404/26350
 * Text Domain: wpse-url-per-size
 * Version:     1.0.0
 */

add_filter( 'attachment_fields_to_edit', function( $form_fields, $post )
{
    // Nothing to do if the attachment isn't an image
    if( ! wp_attachment_is( 'image', $post ) )
        return $form_fields;

    // First option
    $options = sprintf( 
        '<option value="">%s</option>',
        esc_html__( 'Select', 'wpse-image-size-url' )
    );

    // Generate options for all image sizes
    foreach( (array) get_intermediate_image_sizes() as $size )
    {
        // Fetch image url, width and height for the given size
        $src = wp_get_attachment_image_src( $post->ID, $size );

        if( ! is_array( $src ) )
            continue;

        // Generate a single option's value    
        $value = sprintf( 
            '%s %dx%d',
            esc_html( $size ),
            $src[1],
            $src[2]
        );

        // Generate HTML for a single option
        $options .= sprintf( 
            '<option value="%s">%s</option>',
            esc_url( $src[0] ),
            $value
        );

    }

    // Generate HTML for the select box and input text
    $html = sprintf(
        '<select id="wpse-image-sizes" >%s</select>
         <input type="text" id="wpse-image-url" readonly>',
        $options
    );  

    // Handle the select box change
    $html .= '<script>
        (function($){
            $( "#wpse-image-sizes" ).on( "change", function(e) {
                $( "#wpse-image-url" ).val( this.value );
            });
        })(jQuery);
    </script>';

    // Setup our custom form field
    $form_fields['wpse-image-sizes'] = [
        'label' => esc_html__( 'URL Per Size', 'wpse-url-per-size' ),
        'input' => 'html',
        'html' => $html,
    ];

    return $form_fields;

}, 10, 2 );

Using the media_meta filter

This would be similar as the attachment_fields_to_edit example, but displayed within the meta info and without the form fields setup.