A few bits of code for reference, to modify /includes/templates/your_template/sideboxes/tpl_categories.php...

First, the Image Titles mod is now available in Downloads to address the question above.

To skip a certain category (or group of categories) from displaying in the list, find this line near the top of the file:
PHP Code:
    if (zen_get_product_types_to_category($box_categories_array[$i]['path']) == 3 or ($box_categories_array[$i]['top'] != 'true' and SHOW_CATEGORIES_SUBCATEGORIES_ALWAYS != 1)) {
      // skip if this is for the document box (==3) 
    } else { 
and add

($box_categories_array[$i]['path'] == 'cPath=23') or

to the beginning to get
PHP Code:
    if (($box_categories_array[$i]['path'] == 'cPath=23') or zen_get_product_types_to_category($box_categories_array[$i]['path']) == 3 or ($box_categories_array[$i]['top'] != 'true' and SHOW_CATEGORIES_SUBCATEGORIES_ALWAYS != 1)) {
      // skip if this is for the document box (==3), or category 23
    } else { 
If using Cat Dressing, you can replace
($box_categories_array[$i]['path'] == 'cPath=23')
with
($current_path == '23')

Replace the 23 with the correct cPath for your category so it reads (say) 'cPath=4_37'.
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To restrict the display to only certain levels of subcategories, this can be modified as desired:
To only show one level of subcategories, find
PHP Code:
     if (zen_get_product_types_to_category($box_categories_array[$i]['path']) == 3 or ($box_categories_array[$i]['top'] != 'true' and SHOW_CATEGORIES_SUBCATEGORIES_ALWAYS != 1)) {
        // skip if this is for the document box (==3)
      } else { 
and add

ereg("_.*_", $box_categories_array[$i]['path']) or

to get
PHP Code:
     if (ereg("_.*_", $box_categories_array[$i]['path']) or zen_get_product_types_to_category($box_categories_array[$i]['path']) == 3 or ($box_categories_array[$i]['top'] != 'true' and SHOW_CATEGORIES_SUBCATEGORIES_ALWAYS != 1)) {
        // skip if this is for the document box (==3)
      } else { 
Again, if using Cat Dressing, you can replace
ereg("_.*_", $box_categories_array[$i]['path'])
with
ereg("_.*_", $current_path)

This skips the item display if there are two or more _ in the cPath.