How can I use JSON data to populate the options of a select box?

Why not just make the server return the names?

["Woodland Hills", "none", "Los Angeles", "Laguna Hills"]

Then create the <option> elements using JavaScript.

$.ajax({
    url:'suggest.html',
    type:'POST',
    data: 'q=' + str,
    dataType: 'json',
    success: function( json ) {
        $.each(json, function(i, value) {
            $('#myselect').append($('<option>').text(value).attr('value', value));
        });
    }
});