Authentic restaurants in Rome, Florence, and Venice

It would help us give you better answers. for you, if you could clarify what you mean by "authentic" (different people mean different things by authentic).
For example, if they have an English menu, do they not fit into your expectation of "authentic"?

I was thinking somewhere off the beaten path of all the tourists with an authentic Italian menu.

Trattoria Vecchia in Rome and make sure you have reservations. Da’Alvise in Venice, reservations are a good idea there too.

All of the menus are pretty authentic. Unless you think they are offering menus tailored to Am tastes. That is not done. There are different styles or types of Italian restaurants. Ask your hotel for recommendations. They live there.

This thread from a few days ago may help https://community.ricksteves.com/travel-forum/italy-reviews/rome-dining-and-gelato-west-of-piazza-navona. Using the Search Box above, you will find many such threads. In the Filter By box to the left, select ‘Travel Forum’ then ‘6 months and newer.’

Sounds like a great trip Kristine. Here are a couple of recommendations for places I visited last June.

Note some of them require reservations (these are noted):

Sprito Di Vino (Trastevere): http://www.ristorantespiritodivino.com/. Award-winning slow food restaurant with ancient wine cellar. This is a pricey, special occasion restaurant with excellent food and terrific ambience.
I Suppli (Trastevere): https://www.yelp.com/biz/sisini-la-casa-del-suppl%C3%AC-roma. This is take-away food at its best. Pizza by the slice is good, but I would go there for the Suppli (like arancini, only better). If you go, you are not far from Innocenti (delicious Vegan bakery), serving the Trastevere community since 1929.
Enoteca Corsi (Panteon area):http://www.enotecacorsi.com/. We went there first for lunch and loved it so much brought the rest of our group there for dinner. Low-key, great wine and food, very reasonably priced.

I would also highly recommend a food tour. My family and friends and I went on the Eating Italy Trastevere food tour in Rome It was wonderful. These are small tours (our group had 11 people). You visit a number of local establishments from a vegan bakery to a restaurant wine cellar older than the colosseum. The guides are knowledgeable and fun. My only complaint is that there was actually too much food, so take small bites and pace yourself.

Enjoy your trip,
Sandy

Thank you for all your suggestions. I plan on trying a few of them. The vegan bakery is on my list as well.

Rome - Roscioli Salumeria and Armando al Pantheon (need reservations for both)

Trastevere - Da Enzo, I Suppli (best rice balls), Osteria Der Belli

Rome: I would second Armando al Pantheon and add Hostaria Romana...reservations for both.
Venice: Ristoteca Oniga on Campo San Barnaba...probably advisable to make reservations

Florence

Ristorante Toto
Ciro & Sons

Rome

Elle Effe
Pizzeria Emma (owned by Roscioli)

Those are major tourist cities as you know, so don't be put off if a restaurant has a menu with English on it. Frankly, they'd be shooting themselves in the foot if they didn't. My main rule of finding a good restaurant is "The shorter the menu, the better the food."

And never go into a restaurant with someone outside who's urging you to come in.

Thank you for all your suggestions. It will be fun trying some of these places.

In Venice, in the Rialto Bridge area (on the side of the Grand Canal with the fish market) follow the signs leading to Piazzale Roma. There is an out of the way place named Pane Vino e San Daniele located on Calle Dei Boteri. Definitely a local place, good food, good house wine, and not expensive at all. You should be able to use Google Maps street view feature to "walk" to it before you ever leave home.

In Florence we had lunch at a great place. Excellent food, good ambiance, fine wine. Name is Olio & Convivium Gastronomia Restaurant and is on the Pitti Palace side of the river on Via di Santo Spirito. The web site is http://www.oliorestaurant.it/video_eng.php. A bit pricey at lunch and more so at dinner. But the overall experience was worth it. Will eat there again. Check it out and see if what you think

For true Roman pizza near Piazza Navona, go to Baffetto. There's a second location a few blocks away, but I don't think the pizza is quite as good as the original location. It's easier to get seated at lunch hour than in the evening,

Thank you everyone. Great places to check out.

In Florence Trattoria Mario at via Rosina 2/R near Mercato Centrale is wonderful. It is only open for lunch (12pm-3:30pm I believe). There is a nice mix of locals and tourists, be mindful you will be seated at a table with others. They do not take reservations. The ribollita and bistecca fiorentina are delicious. The last time we were there, it was cash only (not sure if that’s still the case). Also recommend reservations for either lunch or dinner at Trattoria Sostanza at via Del Porcellana 25/R. Again, you may be seated at a table with others. They are known for their butter chicken, and they have a meringue cake with berries for dessert that is heavenly. Buon appetito!

Anyone tried Dilla in Rome? Heard it was very good.