Calling a custom category

I am creating a custom template called “city index”. The file needs to include an index for a specific category (among other things). Right now, I’ve figured out how to hard-code the category into the template file:

<?php
query_posts('cat=61');
if(have_posts()) :?>

Where 61 is the category I would like to use.

I would like to replace 61 with a custom field, specified for the page.

So something that lets me use something like:
<?php echo get_post_meta($post->ID, ‘category', true); ?>

where I specify “61” in a custom field associated with the page.

I’m a complete PHP newbie, so what do I need to do to insert the above where “61” is? Will that work? Is there a better method? Any feedback offered is appreciated.