Create a category search within a specific custom field

I have a custom field called ‘state’ and I have created a page that displays posts within a particular state. I have created a search form for categories, but I can’t figure out how to get it to search within the current pages posts (which would be posts for just one state).

I know there are many plugins to do searches, but I am trying to get away from plugins and teach myself a bit more coding. This is where I’m at:

<form name="search" action="<?php bloginfo('url'); ?>" method="get">
<fieldset>
  <select name="category_name">
<?php
// generate list of categories
$categories = get_categories();
foreach ($categories as $category) {
    echo '<option value="', $category->slug, '">', $category->name, "</option>\n";
}
?>
  </select>
  <input type="submit" value="search" />
  </fieldset>
</form>

What it’s doing is only searching the categories and that part is working great. Can anyone steer me in the right direction of a tutorial or how to only search within posts that are currently on the page, which would be posts equal to a certain custom field. That query is done like this:

// args
$args = array(
	'numberposts'	=> -1,
	'post_type'	=> 'post',
	'meta_key'	=> 'state',
	'meta_value'	=> 'Georgia'
);
// query
$the_query = new WP_Query( '$args&meta_key=city&orderby=meta_value&order=ASC' );

Thanks in advance for any assistance,