Is it easy to go on your own or better to sign up for a tour at approx $90 per person? A tour includes Hadrian’s Villa and the other villa and gardens plus bus transportation.
I have only done it on my own and there were no issues, I would save the 90 bucks for dinner. J
I would take the tour - having done this on my own.
I found it a bit inconvenient and, for me, involved getting a taxi from Hadrian's Villa. I haven't looked at the post-Covid transit schedules. Perhaps it is easier now. If transport still involves buses (which includes catching the correct ones) and walking or taxi, I would pay $90 for transport alone. (Of course probably not if I was traveling with a large group at $90 a piece...... I tend to travel solo.)
Trenitalia's train&bus combo ticket from Rome to either Villa costs 3.6 Euro per person, one way. I hope a $ 90 tour is worth the price difference.
The catch is that you have only 1 departure from Roma Termini at 9:03 AM and 2 from Roma Tiburtina at 10:20 AM and 12:20 PM. The Bus #VT002 departs from Tivoli's stations and stops at both villas.
Check the return schedules on www.trenitalia.com. I bet there are 2 rides to Tiburtina in the afternoon and one to Termini in the early evening.
Of course there are many more trains from Rome to Tivoli and back, but you won't find a bus to the Villas waiting outside Tivoli and Bagni di Tivoli stations.
The question is whether you have any money or not? We did Hadrian's and Villa d'Este (independently, Train for d'Este, bus for Hadrian) on different vacations that included Rome. In hot summer sun, the full day on your own is a lot of walking and few dining options. Hadrian's Villa is particularly far from the public bus line. That would be a bit of a death-march day to do both on your own. It is arguable that Hadrian might be unnecessary for those who have seen Pompeii or Ostia Antica. (I mean that as an opinion, not as a cosmic truth.)
I haven't been on a tour, although I DON'T hate being limited to microscopic "free time" on an organized tour. What does the tour say about "Lunch"? Where does it pick you up in Rome?
The following link is more than you asked for, and mostly about Hadrian's, but it might be illustrative. Also a suggestion that you might try the search box here.
https://community.ricksteves.com/travel-forum/italy/hadrian-s-villa-annoyances-and-directions