You can optimize your WordPress search option with categories by adding below code into your WordPress website. You can replace the old WordPress search style in searchform.php, header.php or in sidebar.php (else where the old WordPress search located). By adding/replacing this code, your WordPress search will have additional category search option together.
<form id="searchform" method="get" action="<?php bloginfo('url'); ?>">
<input type="text" name="s" id="s" size="20" />
<?php wp_dropdown_categories('show_option_none=Select category'); ?>
<input type="submit" value="Search" />
</form>
