I'd probably create a database table (if you don't already have one) of all of the cities and rates.You could then use that table to populate the list. When the list is submitted, you can add a recordset to tha action page of the form to filter a recordset based on the submitted value from the list to return the associated rate.
Store that returned rate as a session variable and add a shipping charge rule to the cart to charge a flat rate of the value of that session variable.

on the second line of the filter section, the variable type should be set to Form Value, in the second box, enter the name of the location form element. 
I believe that I followed your steps above, but would like clarification based upon my screen print. One thing that was unexpected was an error that we got when we hit ok on creating a new record set. please see attachments.
this is a link to some screen prints of what we're explaining above: cc3.php
Thanks
Jackie


