Would like to find a location from which to get the best experience of the aquaduct(s).
Aquaduct Park on the Rome Metro lets you get right up next to them. I crossed the Pont du Gard in Southern France through its aquaducts watercourse -- that is as up close as it gets. (don't know if that is still possible)
I agree, Rome is great for this. At Pont-du-Gard last July, you could walk below the aqueduct or raft under it (arrange the raft trip in advance).
If you are in Rome it is super easy to visit the aqueduct park. Here are some directions I wrote a few years ago. Now, I go every trip I take to Rome! http://www.slowtrav.com/italy/rome/dm_aqueducts.htm
I have a feeling there will be a lot of us at the Aquaduct Park this year as it has appeared a number of times on the Forum. I knew about it but always thought it was more out of town than it is. Your instructions were so clear, thank you for that! I am looking forward to being at the park at the end of August.
Don't worry about crowds at the park! It is huge with lots and lots of pathways to take. 8-)
Another clear choice is the Baths of Caracalla, although it was mainly a water destination. Pompeii and Herculaneum have traces of watercourses, and even lead pipes in the ground. I think there are remnants of aqueducts around Tivoli, but can't give you a precise location.
Don't forget the Source of All Wisdom: