Venice and Padua (maybe?)

The Secret Itineraries is just the Doge's Palace complex (including the prisons). San Marco basilica is separate. Entry to the latter is free (hence the queues - try late afternoon), but backpacks need to be stored in a place nearby (3 minutes' walk). There's an admission fee for the upstairs museum, some of which is a bit dull (IMHO), but it's really worthwhile for a closer look at the ceiling mosaics, the original four horses and the balcony view over the Piazza.

There's also a charge for the campanile (bell tower) in San Marco - more queues. It's good, but bear in mind that bizarrely you can't see any canals from the top. My own favourite, and arguably the best view in Venice, is the white church of San Giorgio Maggiore, on its own island directly opposite the waterfront. Take the vaporetto across, and inside the church at the back pay the few € to take the lift to the top of the bell tower for superb views back to Venice and across the lagoon. If you can time your visit so that you're up the tower for the midday bells, you won't forget the experience. :-)

One of the joys of Venice is simply wandering off under your own steam. Personally I would prefer this option - it's good fun getting "lost" (there are always signs back to Rialto or San Marco). This is a great way to get the atmosphere of the place.

I have a minor quibble with thomajd.

It's my experience that day-trippers to Venice don't like to pay admission fees. For anything.

That's why I've never seen the queue for the Doge's Palace anywhere remotely as long as the queue for the basilica, where entry is free. And why I'd encourage you to visit the basilica first (do not forget the upstairs museum!), Doge's Palace second, Correr Museum if time permits.

As for Padova: I understand the temptation of "Giotto Under the Stars." Especially if you want to spend more than 15 minutes in the chapel. But if you want to see other sights in Padova, you'll be limited to the outdoor attractions, given the time. Unless you leave for Padova early enough to take a pretty big bite out of your time in Venice.

Plus, trips to both Padova and Torcello, and a morning and afternoon in Piazza San Marco will greatly limit your time simply wandering Venice. And wandering is the best way to avoid the Beaten Tourist Path.

If you decide on Torcello, you might as well stop at Murano. Not for the glass shops or glass-blowing exhibitions, but for the church of SS Maria e Donato with its beautiful floor and apse mosaics (and alleged and partially hidden dragon bones mounted on the right side wall under the apse. It must have been a baby dragon). This church is only about 200 years younger than the ones in Torcello.

Whatever you decide, please do get off the Beaten Tourist Path in Venice. There are areas in northern Canareggio (north of the Ghetto, for example), where you can be the only people on the street. And that's the closest I've ever been to being in a time machine.

While you're there, and to bring you kicking and screaming back to the 21st century, consider taking a free gander at Scotland's entry to the Venice Biennale, Rachel Maclean's divisive film "Spite Your Face" in the Church of Santa Caterina on... Fondamenta Santa Caterina.

So many choices, so little time...

A half day trip to Padova is easy if you stay in a hotel close to Venice railway station but always impossible if you stay somewhere at the other end of the city.

I have a minor quibble with thomajd.

It's my experience that day-trippers to Venice don't like to pay admission fees. For anything.

That's why I've never seen the queue for the Doge's Palace anywhere remotely as long as the queue for the basilica, where entry is free. And why I'd encourage you to visit the basilica first (do not forget the upstairs museum!), Doge's Palace second, Correr Museum if time permits.

Yes, I see where you're coming from on this. By the time the OP came out of the Palace, the daytrippers would have descended on the Basilica in their hoards. It might help to do the Palace and the Basilica on separate days, but the OP isn't awash with time.

Also agree that with just 3 days the Correr Museum is a "nice to" rather than "need to".

I think you mean "almost" impossible.
And I think that may be over-stating it.

But if you do the night trip, and you want to take the vaporetto from the Venice train station back to your hotel, you should check when the regular service ends and the "night service" (about once an hour) begins. I think it's later than your return, but worth checking.

There's no place in Venice proper you couldn't walk to, eventually, from the train station. On the other hand, it's very easy to walk in circles in Venice, especially at night. I've done it. Campo Santa Maria Formosa--again???

So walking might take longer than you think. Unless, as noted, your hotel is close to the station.

And as I said, thoma, a minor quibble. But I'm also less keen on the Doge's Palace than most. From the inside, the Bridge of Sighs seems like a short hallway. Kind of like it does from the outside. The prisons and some other interiors are interesting (my, what big globes you have!), most of the art isn't.

After all the very detailed and amazing advice that has already been given, I feel a bit "nervous" to join this post so late and give my meager advice ;-). I was in Venice last year for a week (not my first time there, and certainly not my last time, as I really really like Venice), and I still havent been to all the places I would like to see. So yes, with 2.5 days, you wont be able to see it all and you will have to make choices, and you know yourself what you feel most attracted to, and what is most important to you.

Yes there are some wonderful palaces, museums, buildings, exhibitions, churches etc. in Venice. But for me, what makes the city really unique and special, is the lack of road and cars and traffic noise. The only way to get around is on foot and by boat, and that makes for such an unique experience. By all means visit places like the Doge`s palace, but also allow enough time to simply wander around and get lost. Even from a very very touristy place like St. Marks it doesnt take more than a 5 minutes walk and there wont be many other tourists left. I would also recommend to get a 3 day Vaporetto pass, so that you can have unlimited use. Spending 1-2 hours on a Vaporetto is one of the best and most relaxing way to see Venice in my opinion. Maybe take the Vaporetto to the Lido (not because you want to spend time there, but because the boat trip back to Venice is quite spectacular) and then onward on the Canale Grande to the train station.

If you like food (like I do), Venice is fantastic. Yes, there are many horrible tourist traps, but they are also quite easy to avoid, and especially if you like fish and seafood, you will be in for a treat. You might also consider doing a guided "eating tour" around Venice. You will eat plenty of great food and drink wine, and have some interesting comments about life in Venice etc. But of course it wont be free.

"I think you mean "almost" impossible"
Of course! Thanks for the correction.

BTW: I like to stay at hotel Stella Alpina, in a quiet area, less than 10 min from the railway station platforms (no steps, no boat transfers with all the luggage).

Thanks for all the advice!!

My wife and I are staying at a AirBnB in San Polo fairly close (but not too close!) to the Rialto Bridge. Really good price too. Like 115 euro/night and its the entire apartment!

I absolutely agree with you all that just walking around is really the way to go. That is definitely on the agenda. And you're right, there are just SOOOOO many places to go see and you can't do it all, and the hard part is figuring out what you're going to leave out. Thanks nathalie2, for your advice! I haven't considered getting a vaporetto pass, but thanks for bringing it to my attention. I will definitely consider it, at least a 24-hour pass!

I'm thinking I agree with the idea we might want to split up San Marco & the Doge's Palace. One of the things that I'm trying to figure out is what to do on that last day - the 1/2 day before our plane leaves (at 3:30p). I'm thinking an early visit to San Marco's might be the perfect fit, no??

Lastly, given my affinity for art, history, and churches (and less crowds, the better.....I get it, it's Venice, but you know what I mean), and given my time constraints, is Torcello skippable? Just from reading what everybody has posted, I think I would love Torcello....but.....I'm thinking that in order to make it happen, I'll most probably have to skip the Accademia. So which is it?

Oh and Padua, I think if we do it, we will have to do the evening visit. I just don't see another way of fitting it in. Which is unfortunate, b/c I've heard that the University tour is really excellent as well. And that's to say nothing of the churches and the piazza, etc.

All good advice from nathalie2, I would say. :-) It has taken me six visits to Venice to tick off everything on my "to do" list. OK, there have been some repeats, and only once did I stay for more than three days. But it confirms what you say (and why I always recommend a stay of four days - two for the tourist stuff, one for your own stuff, and one for the islands - and all before day trips to other places).

Good advice on the vaporetto pass. Good routes to experience are those which include the full length of the Grand Canal and/or the full circuit of the city.