Just to double check the information you have for getting to Tivoli by public transportation - take the Blue Metro Line B to the Ponte Mammolo station and from there you can get the blue Cotral bus to Tivoli. You can visit Villa d'Este first and when finished take the local orange bus out in front of Villa d'Este to Villa Adriana. This bus stops, if I remember correctly, in front of a cafe (check with driver), and then it's a short walk to the entrance of Hadrian's Villa. An orange bus from in front of the cafe can take you back to Ponte Mammolo or you can walk to the main road, Via Tiburtina, and catch the blue bus, which runs more often.

We did not use public transportation. This was one of the few times we used a guide who drove us from Rome and conducted the tour. Villa d'Este does not really warrant a guide but Hadrian's Villa is a massive complex and difficult to navigate and appreciate to the fullest without some professional guidance. At minimum, be sure to buy a guide book that identifies and explains what you are seeing and/or check out these sites for self-guided walking tours: http://tinyurl.com/7nndp http://tinyurl.com/9fk4b

Here is the official web site of Villa d'Este, which you might find useful: http://www.villadestetivoli.info/infoe.htm

Hope that helps, Don, enjoying Rome