Using the venue slug as a CSS class

// Get the venue ID for this event
$venueID = tribe_get_venue_id();

// Check that a valid venue ID was returned ("0" may be returned if none is assigned)
if (is_numeric($venueID) and $venueID > 0) {
    // Get the slug
    $venue = get_post($venueID);
    $venueSlug = $venue->post_name;
}
else {
    // Otherwise, set the slug to an empty string
    $venueSlug = '';
}

// Take $venueSlug and use as CSS class
echo '<div class="'.$venueSlug.'">'; // etc...