This code snippet replaces the full address with the city name in the User Location field.

um_user_locations_map_args_customize_06.php

<?php

/**
 * Change the user location field value. Save only a city.
 */
add_action( 'wp_footer', function () {
  ?><script type="text/javascript">
    var currentLocationField;
    jQuery( '.um_user_location_g_autocomplete' ).on( 'click', function() {
      currentLocationField = this;
    } );

    // on autocomplate.
    wp.hooks.addAction( 'um_user_location_after_location_field_set_by_autocomplete', 'um_user_locations', function ( place ) {
      for (const component of place.address_components) {
        if ( 'locality' === component.types[0] ) {
          currentLocationField.value = component.long_name;
          break;
        }
        if ( 'postal_town' === component.types[0] ) {
          currentLocationField.value = component.long_name;
          break;
        }
        if ( 'administrative_area_level_3' === component.types[0] ) {
          currentLocationField.value = component.long_name;
        }
      }
    } );

    // on geocode.
    wp.hooks.addFilter( 'um_user_location_formatted_address_set_by_geocode', 'um_user_locations', function( formatted_address, results, position ) {
      for (const component of results[0].address_components) {
        if ( 'locality' === component.types[0] ) {
          return component.long_name;
        }
        if ( 'postal_town' === component.types[0] ) {
          return component.long_name;
        }
        if ( 'administrative_area_level_3' === component.types[0] ) {
          return component.long_name;
        }
      }
      return formatted_address;
    } );
  </script><?php
}, 20 );

This gist is a part of the article User Locations - Hooks

You can add this code to the functions.php file in the active theme directory. Skip the opening <?php tag.