Here’s the working answer for future reference.
<p>
<label for="<?php echo $this->get_field_id('select'); ?>"><?php _e('Choose A Page:', 'check_avail_widget'); ?></label>
<select name="<?php echo $this->get_field_name('select'); ?>" id="<?php echo $this->get_field_id('select'); ?>" class="widefat">
<option value="Select A Page">
<?php echo esc_attr( __('Select A Page') ); ?>
</option>
<?php
$pages = get_pages();
foreach ($pages as $page) {
echo '<option value="'.get_page_link($page->ID).'" id="' . $page->post_title . '"', $select == get_page_link($page->ID) ? ' selected="selected"' : '', '>', $page->post_title, '</option>';
}
?>
</select>
</p>