May I start with saying that I really like the K2 tools!

I am trying to do a background colour (different) for each tag.

I am trying to change the file default.php in the folder /mod_k2_content/tmpl/Default/default.php however the change I am doing is not reflecting in the main page.

<a href="<?php echo $tag->link; ?>" id="tag<?php echo $tag->id; ?>"><?php echo $tag->name; ?></a>

What I basically would like to add is the style sheet id="tag"

Would appreciate if you can pinpoint if I need to edit another file.

The main page might be the component, take a look here on K2's file structure and overrides.
getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates

This will help you locate and override the files you need to edit.