Where to spend two nights between Rome and Venice?

might as well Orvieto since it is on the way

Orvieto is lovely and well worth an overnight or two.

Orvieto is a great choice--I speak from experience having stayed a couple of nights there in October 2016. The cathedral there is spectacular. You can see a lot there is a little time. Don't miss walking into the well, and the guided tour of the underground chambers (not caves precisely since they are human-made).

Thanks! Orvieto does seem just about perfect., assuming we can get accommodations. We are also considering Tivoli, Lucca, and Padua and Bologna , all of which fail to meet one criteria or the other. Any votes for them?

Well, if you want great food - Rick - on his podcast, just had a food guy on and he said Bologna was his #1 fav destination for food. Look to the left of the screen - hit Watch Read Listen and go to Listen to the Radio Show - the current episode is the one you want to listen too. (Program 513 if you don't see this before a new one pops up as they are weekly).

We had a few scant hours in Bologna (a morning) on our first trip in '08. Our trip next year is going to be to Venice for Carnival, and I was trying to figure out some other places to visit with our extra days, and after listening to the guy rhapsodize about the food in Bologna, I think we are going to head back there for a few days and just eat.

There is also some neat architecture there - it even has its own leaning tower! http://www.italymagazine.com/news/leaning-tower-bologna-torre-garisenda and...has the 10th largest church in the world (by volume!) https://en.wikipedia.org/wiki/San_Petronio_Basilica

I especially like (in the radio show) where he says if he knew he only had a week to live, he'd say goodbye to NYC and fly to Bologna and spend the next week eating a diff pasta dish every day. :)

I was going to suggest Bologna as it seems to fit most of your criteria. If you have a full day available (it starts first thing in the morning and goes through the afternoon), we really enjoyed our food tour by Italian Days that left from Bologna. We did it a few years ago and they only offered the tour from Bologna, but they have now expanded and offer something similar in multiple cities. It is not cheap, but they took us in small vans to a parmigiano reggiano cheese, balsamic vinegar and prosciutto factories followed by a family style meal that had more food than we could ever finish and was a lot of fun. Only problem we had was that we did the tour on our first full day in Italy and the food coma and jet lag combination knocked me out!

http://www.italiandays.it/

Thanks for your inspiring answers. Still brainstorming though. Considering we will basically be zombies after our flight from the US, what about the idea of going from FCO to some kind of a refuge somewhere just outside the ring of Rome...the coast? Tivoli? Ostia Antica? To walk, see gardens, ruins. Two nights. Then fly up to Venice day before the tour start.

I wouldn't fly to Venice. The train (city-center to city-center) takes about 4-1/2 hours. Dealing with airports will make flying take about the same amount of time.

Except for Tivoli, I've been to all the places mentioned in this thread, and there are not really any bad choices. There are time/cost factors affecting some of them, however:

Lucca: Off the main rail line. 4 to 4-1/2 hours, and if you don't buy your ticket in advance (guess accurately or the ticket will be worthless), you'll pay a pretty penny for it, because the Rome-Florence leg is on a Freccia train.

Padua: Also about 4 hours, and the entire trip from central Rome is on a Freccia train, thus probably costly if you make a day-of-travel purchase. [Book the Scrovegni Chapel ahead of time.]

Bologna: About 3 hours, but again there's the Freccia cost to consider.

A quick spot-check indicates that day-of tickets to the above places on fast trains (and you wouldn't want to take a slow train) will probably cost 50 euros per person, or more.

Ostia Antica is very near Fiumicino Airport. I don't know where the best lodgings are located, but I'm sure there are options not far away. I've just spent a few hours at the ruins while staying in Rome. I don't know what one would do for 1-1/2 days there.

Orvieto I love. It may not be Bologna, but it has plenty of good restaurants. There's lots to do there for 1 or 2 days, and the town is very pretty.

Orvieto it is. Thank you everyone. Orvieto looks like a great place to adjust to a new tîme zone while immediately immersing ourselves in the magic of Italy.