We will be in Tivoli for less than a full day - can you tell me if you would rather visit Villa d'Este or Hadrian's Villa?
If you prefer old rocks, go for Hadrien, if you're more into rennaissance gardens, go for Este.
Though you could do both in 5-6 hours.
I have a personal preference for Hadrian
Do both - you have the time. Both are very difference. But the gardens are very interesting. Great photo opportunities.
The two sites are not comparable. D'Este takes much less time and shoe leather. Hadrian is tough on a hot sunny day, d'Este much cooler and shadier. Public busses between the two are time-consuming, especially if you accidentally descend at the wrong stop.
Does your first sentence mean you have an overambitious "Rick Steves" day planned, with three widely separated, famous sights to see? Start planning your fallback position now, for when public transportation builds nostalgia for your Chevy Suburban tank back home ...
Thank you to everyone for taking the time to answer.