Swapping wp_dropdown_categories function with wp_category_checklist

As you are not working with the default categories but with another taxonomy instead you must not use wp_category_checklist(). Instead you should probably be using the more generic wp terms checklist(). The signature of this function also differs from the one of wp_dropdown_categories(). And the arguments array takes completely different options.

You shlould start with the following code and then adapt it according to your needs:

require_once ABSPATH . 'wp-admin/includes/template.php';

wp_terms_checklist( 0, array(
    'taxonomy' => 'acadp_locations',
) );

I am not sure if wp_terms_checklist() is going to suit all your needs. Maybe you have to write a custom Walker (Start with extending Walker_Category_Checklist()) to adapt the output to your requirements.