The first example below will print a list of the available spaces for each datetime, located after the ticket selector. The second example will add a "spaces left" item next to each datetime listed for the event. Requires Event Espresso 4.

ee_print_remaining_tickets.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

// print the remaining tickets left for each datetime

add_action( 'AHEE__ticket_selector_chart__template__after_ticket_selector', 'ee_print_tickets_left_after_selector', 10, 2 );
function ee_print_tickets_left_after_selector( $EVT_ID, $event ) {

    echo '<ul style="margin-left:0;">';
        $datetimes = $event->datetimes();

        foreach($datetimes as $datetime){
            if ( $datetime instanceof EE_Datetime ) {
                $dtt_name = $datetime->get('DTT_name');
                $name = !empty($dtt_name) ? ($datetime->name()) : 'this event';
                $limit = $datetime->get('DTT_reg_limit');
                $remain = $datetime->spaces_remaining( true );
                $remain = $limit == EE_INF ? 'a lot of' : $remain;
                if ( $datetime->sold_out() ) {
                    echo $name . ' is <b>sold out</b>';
                } else {
                    printf( _nx(
                        '%1$sThere is one space left for %3$s', 
                        '%1$sThere are %2$s spaces left for %3$s', 
                        $remain, 'event ticket info', 'event_espresso' ),
                        '<li style="list-style-type:none;">', $remain, '<span>' . $name . '</span></li>'
                    );
                }
            }
        }
    echo '</ul>';
}

ee_remaining_spaces_reg_limit_after_each_datetime.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

add_filter(
    'FHEE__espresso_list_of_event_dates__datetime_html', 
    'ee_print_avaialble_datetime_reg_limit', 
    20, 
    2
);

function ee_print_avaialble_datetime_reg_limit($html, $datetime){
    $remain = $datetime->spaces_remaining( true );
    $remain = $remain == EE_INF ? '' : $remain . ' left';
    $html = $html . '<span class="ee-remaining-date">'.$remain.'</span>';
    return $html;
}