[Infinity178]

1. Изменить DOM объект для поиска списка

<script type="text/javascript">
ymaps.ready(function () {
  var map = new ymaps.Map('YMapsID', {
    center: [55.753559, 37.609218],
    zoom: 9,
    type: 'yandex#map',
    behaviors: ['default', 'scrollZoom']
  });

  new RegionSelector(map, data, $('.selectbox'), $('#cities'));
        });
</script>

2. Изменить option на DOM li

ptp.onRegionChange = function (e) {
    var self = this,
        regionName = $(e.target).find('li.selected').text(),
        region = this._data.regions.filter(function (region) { return region.name === regionName })[0],
        cities = this._data.cities.filter(function (city) { return city.region === region.id });

    this._cities
        .empty()
        .html(this.createSelectOptions(cities))
        .trigger('change')
};