Day trip to Hadrian's Villa and Villa d'Este from Rome using public transport?

We followed the directions in Steves' Rome guidebook. Requires the train and a couple of buses but his directions are good. The Villa dEste can consume a lot of time and seeing both makes for a very full day.

Having been to both, I would not try to do both in one day unless you at least use a taxi between them. Hadrian’s Villa benefits from a guided tour, IMO, and is a bit remote from the train station.

Villa d’Este is an amazing estate/garden/palazzo and is walkable from the station. By the time you walk there, tour, and have some lunch or a rest, you may be too tired to tour another place anyway.

Only go if the weather is good. Neither is much fun in the rain.

https://community.ricksteves.com/travel-forum/italy/hadrian-s-villa-annoyances-and-directions

We did this a few years ago and had no problems nor regrets. We took a bus from Rome to Tivoli following Rick’s advice and walked over to tour the Villa. I recall lovely murals in some rooms but it didn’t take too long to complete. As much as I love gardens, it really didn’t take too long to feel we’d had a good visit, which frankly surprised me at the time. We walked a few minutes to catch the bus to Hadrian’s Villa, had a quick lunch at a restaurant just outside the entrance, and spent some hours walking all over the grounds. It is very large. Then bus back to town and back to Rome. We enjoyed our day, didn’t feel rushed or fatigued. This was all before timed entry tickets so our mileage varied. Very enjoyable all the way around. Safe travels.