Venice - book a tour or explore on our own?

I think mostly on your own with one or two carefully selected tours that will offer something you can't do on your own.
For example an early access tour (where you go somewhere popular with fewer crowds). I have not done one in Venice but in Rome the Walks of Italy Pristine Sistine is worth every penny (you get into Vatican before crowds and see Sistine Chapel without the sardine effect). I like Walks of Italy in general - see what they have in Venice

Also maybe a food tour - a good one will take you to places you wouldn't find on your own and encourage you to try new things.

The reason for my preference for mostly on your own is that I think I experience more when I am fully alert to getting around, doing the research, and immersing myself instead of relying on a guide. I learn better doing it myself vs hearing it from a guide. Plus I best experience a city by wandering and getting turned around, which you don't need a guide for ;)

Thanks, Mira! Just booked the Vatican tour as recommended. Venice looks good, also. Appreciate the advice!

We did the Secret Itineraries through the Doge's Palace and enjoyed that. But for the most part in Venice did everything on our own. We tried to do the free walking tour but the tour guide never showed up. I guess you get what you pay for :)

You will love the Vatican tour. And well worth seeing it with few people around. When we came back around to leave got stuck in the Chapel as the exit they use was being used for dignitaries - we were stuffed in the Chapel like a can of sardines - not pleasant.

We mostly wander around on our own, but did book an afternoon/evening walking tour of Venice that included a Gondola Ride.
Found it thru viator.com - they are a tour consolidator.
We all really loved the walking tour and the guide took us all over - very informative.
We bought a 3 day vaporetto pass and it "paid for itself" with just a few rides.
RS recommends taking the vaporetto on the grand canal - from one end to the other - it was wonderful for taking photos and seeing the sights.
We went on our own to Murano (stopped at the cemetery island (very pretty and interesting), another day we went to Burano.
Go to the top of tower on San Marco Square - early in the day is best - wonderful views.

We have been twice and love getting lost in Venice. I think a food tour would be amazing. They have great food. Definitely do a chichetti crawl as Rick recommends. St. Marks Cathederal, Doge's Palace, Friar Church, Rialto Bridge, Morning Fish Market near the Rialto, a trip up and down the Grand Canal. Gondola Ride in the day, at night, you don't see the beautiful buildings. Get lost! Skip the Gugenheim Museum, it is filled with Modern Art, which is not why I came to Venice.

Try a chichetti crawl by visiting different places. Each chichetti pub has their specialties, fried, sandwiches, etc. My favorite is Osteria al Portego. https://www.tripadvisor.com/Restaurant_Review-g187870-d1034685-Reviews-Osteria_al_Portego-Venice_Veneto.html Their Tiramisu is amazing!

If you have a chance, visit Torcello in Venezia (near Burano). This is the oldest part, and has a couple of churches with beautiful mosaics.

We also took the Viator walking and gondola tour. It was really good, and a good price. The reason we did it was to have a gondola ride for WAY less than just walking up and taking a gondola ride.
The ride itself was only about 20 mins.; but so relaxing after walking a lot on a hot dayt!
The walking tour guide was really knowledgeable.
I recommend it.
You can't get lost in Venice: it's an island, so walk everywhere.

I heartily recommend the cichetti tour with Row Venice. A great way to get away from the crowds and see some of the real Venice. The rowing was exceptional fun, our guide extremely knowledgeable, and the canal side stop for cichetti and wine was delicious! This was the first thing we did upon arrival in Venice and it gave us this feeling as being part of the city for the rest of our stay.

Excellent advice from all. Much appreciated, and we're excited to get traveling!