How to add search by custom field/taxonomy option in header

Hello guys,
I want to setup an advanced search under the header. How can i add a custom field/taxonomy to the advanced search? I have used the following code to add a taxonomy called “City” in the search. It displays the list of cities i added but when i chose a city it returns the ID of the city instead of the name. So the search is not working e.g it outputs
wordpress/?s=&cat1=&tx_city=78
78 is the ID of that option. The search works fine if ” tx_city=NameOfCity “. Is it possible for it to return the name of taxonomy option instead of its ID or is there any other way to do it?
Thanks
[code title=”Adding taxonomy field in search”]
<div class=”col-md-3″>
<select name=”tx_city” class=”form-control”>
<option value=”0″>
City
</option>
<?php echo $CORE->CategoryList(array(0,false,0,’city’)); ?>
</select>
</div>
[/code]