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.