This code snippet replaces a link on the widget calendar with one that points to the a category for one of the events running on that date

widget-calendar-link.php

<?php
/**
 * This is a code snippet that will work with Event Organiser 1.6+
 * At time of writing 1.6 is still in beta.
 * This should go in a separate plug-in or functions.php 
 * Do not change the Event Organiser files - changes to EO will be lost when you upgrade.
 *
 * This code snippet replaces a link on the widget calendar with one that points to the a
 * category for one of the events running on that date. It priorities the term 'foobar'.
 * The link appends ?ondate=[some-date] to filter by events active on that date (i.e. 
 * the date on the calendar)
 */

add_filter('eventorganiser_widget_calendar_date_link', 'myprefix_link_to_event_cat',10,3);
function myprefix_link_straight_to_event( $link, $date, $events ){
       //Note $date is a datetime object corresponding to a day in the widget calendar
       //$events is an array of events. Currently this non empty, but I might filter all dates - so in 
       //later versions it might be non-empty. I recommend assuming it might be and do a sanity check

       //Sanity check
       if( !$events )
           return $link;

       //Let's get all the event terms:
       $event_cats = array();
       foreach( $events as $event ){
          $terms = get_the_terms( $event->ID, 'event-category' );
          if( $terms)
             $events_cats += $terms;
       }
    
       //If no there are no event categories, abort
       if( !$event_cats )
          return $link;

       //Extract the term slugs
       $event_slugs = wp_list_pluck( $event_cats, 'term' );

       //If 'foobar' is present - use that
       if( in_array('foobar', $event_slugs) ){
           $slug = 'foobar';
       }else{
           //Foobar not present, just pick another category
           $slug = array_pop( $event_slugs );
       }

       //Get link to that category, and append 'ondate'
       $link = add_query_arg('ondate',$date->format('Y-m-d'), get_term_link($slug, 'event-category'));

       return $link;
}
?>