A week in Venice or beyond?

The first option sounds best since it almost always takes more time going from Point A to Point B than anticipated. Not to mention the packing and unpacking thing. Very easy to spend a week in Venice. Simply walking, holding down a chair with a glass of wine (at a back street café), and people watching is a joy in Venice. Side trips to Verona (really great food), Padova, Murano / Burano / Torcello, are all easily done in a day.

Yes, Padova is worth a full day. Get a reservation for the Scrovegni Chapel to see the Giotto frescoes. The center is interesting, especially the outdoor markets and the Anatomy Theatre in the University. There is a street car that runs between the train station that runs to the center of town you can use to hit all the sights. A day pass isn't much (less than a single vaporetto ride in Venice). The Regionale Veloce trains are only about 5 euro and get there just as fast as the Freccia trains.

I think you could also do a day trip to Ravenna. That and Padova would be my top priorities, a day for each. If you want to see the Scrovegni Chapel, you need advance reservations. The three islands of the Venetian Lagoon are another day. Don't omit Torcello, in my opinion, the most interesting of them.
You might also look into the cruises on the Brenta Canal. They are done by two different companies, with very similar itineraries and for similar prices. You have a choice of a full day or half day. They make some stops at Palladian villas, through which you are taken by a guide. Having done the full day, I would say half is enough. We started in Padova at 8 A.M. After we got to Venice, we were bussed back during rush hour, returning after 7. Made for a very long day. In planning, you need to realize that they start in Venice on alternate days. Or, I think you can join the cruise for the afternoon and end in Venice on the other days. I don't remember the company names, but you can get them by googling "Brenta Canal cruises." Their sites include detailed itineraries.
Bassano del Grappa and Marostica are other nearby towns of some interest.
There, your week is almost filled. I, personally, wouldn't try to do any of the more far-flung places. Rome is too dense for just a day or even a couple, as is Florence. Civita, not worth the effort even if you were staying close by. Lucca, Siena, and Pisa are too far for day trips. Too much traveling for too little time there.

Thanks all for the excellent suggestions so far!

I love Venice but have not previously spent more than a day or two. I like architecture, art, scenery, taking photos and food. I have been to Civita and love it. I was thinking two nights in Florence, Siena or Pisa. The latter because my daughter asked about the tower.

But we will be going back to focus on Italy another time!

I'm not crazy about the idea of day trips from Venice, since it takes time to get to the train station and then it can be a longish ride to anywhere else. The only upside is that you're in Venice in the evenings, but perhaps too tired to enjoy it.

Last year I used Bologna as a base and became enamored with the city itself. The train station is an easy walk from the center, there are few tourists, compared to other towns, great food and drink, of course. It's easy to day-trip to Ferrara, Padua, Florence, Verona, and (highly recommended if you haven't been) Ravenna. After Bologna, I made my way south, stopping for 2 nights in Florence, 1 in Assisi, then 3 in Orvieto. From there, I took the train to Termini and the Leonardo to FCO.

Food for thought.

Thank you all for the suggestions. We will be staying in Venice to enjoy it after the day trippers and cruse shippers have left. We also will be taking a day to visit family friends near Pordenone.

I will definitely plan for at least one day trip. Possibly to Verona. Daughter will be interested in the Shakespeare connection.

Have given up the idea of Florence and beyond for the trip.

Grazie!

Padua - Vicenza - Verona - Mantua - Modena - Bologna - Ferrara - Padua is a nice circuit from Venice.
I don't think you have time for all this. Trains are excellent in this part of Italy, everything is very close.

If you choose to return home from Venice may I suggest ...
Venice - 3nts
Padua - 2nts - with day trip to Vicenza
Verona - 2 nts - with day trip to Mantua

If you choose to return home from Rome may I suggest ...
Venice - 2nts
Verona - 2nts
Florence - 3nts - with day trip to Siena