Роман

Ну может я не совсем правильно понял структуру, но я бы сгруппировал так:

$stats = array();

$stats_by_group_id = array();

foreach($stats['response'] as $day_stats) {
    $date = new DateTime($day_stats['day']);
    $date = $date->format('Y-m-') . '01';
    
    foreach($day_stats['cities'] as $id_city => $day_stats_city) {
        if (!isset($stats_by_group_id[$id_city])) {
            $stats_by_group_id[$id_city] = array(
                'date' => $date,
                'visitors' => 0,
                'cities' => 0
            );
        }

        $stats_by_group_id[$id_city]['visitors'] += $day_stats_city['visitors'];
        $stats_by_group_id[$id_city]['cities'] += $day_stats_city['cities'];
    }
}