The following hotels in Frascati offer a shuttle service to Villa Mondragone.
Hotel Flora ****
https://www.hotel-flora.it/en/
info@hotel-flora.it
Hotel Colonna ***
https://www.hotelcolonna.it/en/
hotelcolonna@hotelcolonna.it
Villa Mercede ****
https://www.villamercede.com/
info@villamercede.com
Hotel Cacciani ***
http://www.cacciani.it/hotel/
hotel@cacciani.it