This is probably
the most common question asked in this forum, as well on the web, regarding Ajax. Do a search and you will find hundreds, if not thousands of solutions.
One of the easiest, should you adopt jQuery to do you Ajax for you (highly recommended), is to use the jQuery load() method as follows:
where
/fetchCities is a server-side resource (perhaps using
Servlets and JSP -- which I know you know) that returns the formatted HTML options elements.
But looking around, you'll find that there are many different ways to do this.