From Rome to Villa d' Este

No need for tickets in advance. Take the train and then the bus. I think it is covered in the Rick Steves' Rome guide book.

Villa d'Este is in the town of Tivoli, there are a couple of interesting sights there. Have a look at the Villa Gregoriana and the waterfall. Some nice walks through the town, lots of restaurants and cafes.

The only piece of info probably not covered by RS is a very recent change in how you buy your regional train ticket, and you will need that to get to Tivoli, where Villa D'Este is: when buying said ticket (be it from a vending machine, a mobile app or an actual ticket office) you will need to specify the date in which you want to travel, and you will only be able to use the ticket on that day - no different than in most places, really, but I think it's better to know in advance!

All trains to Tivoli depart from the train station at Roma Tiburtina, except for one that leaves from Roma Termini in the early morning, but caters to commuters, so I would avoid it. There's a train each and every 30 minutes, roughly, and the ride is about 1h (not all trains end their ride in Tivoli: some continue to Avezzano or Pescara, so be careful not to end in another region!).

October is a lovely time to go. We always take the train but be aware that it is a bit of a walk from the train station to the entrance, about 20 minutes. It can be confusing the first time, so print out a map from GoogleMaps unless you have a smartphone to navigate with.

We prefer the train, but it should be noted that the bus (from Ponte Mammolo) goes nearby (but not right beside) Hadrian's Villa on the way to Villa d'Este. In fact, it's very difficult to see both attractions in one day, and Villa d'Este is the better. But I wanted to make sure you didn't completely overlook Hadrian's. The bus can be distressingly crowded, also. But maybe better in October than in high season.

We took the bus from Rome to Villa d'Este. After seeing the villa (it didn't take all that long) we walked back a short bit and grabbed another bus to Hadrian's Villa where we spent several hours...it's a very large area...then took the bus back to town, where we caught the return bus to Rome. It was indeed a very crowded bus in the late afternoon---SRO. ( I was about the last to board the bus and rode back to Rome practically squashed against the windshield...luckily, the driver only stopped talking on her cell phone once to advise me that I couldn't do that ). A nice restaurant across from Hadrian's Villa made for a pleasant lunch break before entering the grounds. It was a rewarding day.