Travel in northern Italy

Whether you can do this without a car depends on what "near Treviso" means. Will you be within accessible distance to a train station? If so, you're in business. There are excellent daytrips to Verona and Padova, among many other places, but to me, part of the charm of Italy is slowing down, exploring and enjoying where you are. IMHO, daytrips are good to have in your backpocket as options if you get bored with where you are.

Michael,
I'm going to be in a converted farmhouse that's 3-4 miles outside of the "center" of Treviso (off of Via Callalta/SR53). So immediate access to public transportation? Not so much. I think that once I get into Treviso I could move around from there, but I'm not sure of the best way to go about this. There's only so much to do at the farmhouse, so we'll definitely be doing the day-trip thing.

I see. How do you plan on getting to/from the agriturismo?

if you have a car (which I would recommend) you could also see Bassano del Grappa, Mantova, or Cividale, all of which are wonderful towns. I would also second the Padua recommendation - but be sure to make reservations in advance for the Scrovegni Chapel.
I would also HIGHLY recommend lunch at Fermi in Treviso. We had a wonderful lunch there in September and I bought several items from their store. Just fantastic!

Gotta admit ... I was hoping for an easy "don't worry, just call a taxi" answer something that would get me into Treviso and I could bus-n-train out of there. But I'm sensing that a rental car is both necessary and more desirable to give me a bit more flexibility and control.

P.S. to ekc ... Thanks for the dining rec!

Hi Gayle, if you are interested in architecture, you would probably enjoying visiting a Palladian villa in the countryside such as Villa Pisani. However, if you visit Vicenza (worth the trip and easy day trip by train from Treviso), you will get your fill of Palladio.