Since its your first time in Italy I would do guided tours with Viator for the sights only. They have great day tours leaving Rome. check it out, they have multi- days as well. My favorites are Florence, Rome and Capri.

I either eat where tripadvisor says to eat, or if lack the time or energy to research it, I head for the noisiest restaurant. If is noisy it will be enjoyable.

I think Venice is the hardest to follow these rules as the maze of streets makes finding a noisy place and the general "rip-off" there will be another 60,000 tourists tomorrow attitude gets in the way.

Generally I like towns and cities which are not the prime draws for tourists and so would look outside Florence and Rome for the best meals.

Florence and rome both have tons of good local restaurants from budget prices on up.

There are a couple of rules:

Don't eat immediately adjacent to any major sights
Don't eat at any place that has tours trying to drag you in
Don't eat any place with menus in 8 different languages
Don;t eat any places with pictures of the food
Do eat at places that are patronized by locals - and with staff that seem to be family members

One of our best meals in Rome was in a small place on a back street we fell into when it started to pour unexpectedly. The menu was handriwtten based on what they has that night, the meal was really wonderful, they brought extra (unordered and uncharged) veggies and the wine was from the vineyard of Uncle someone while the dessert - tiniest strawberries - were from the farm of cousin someone else. We loved it so much we went back 2 nights later.

Rome - Borghese gallery, churches (all of them)
Florence - Brancacci chapel, Santa Croce
Venice - Ca d'Oro, Miracoli church, Torcello

In Florence, loved Osteria Cinghiale Bianco http://cinghialebianco.com/. It is across the river in the Oltrano district- very walkable from central Florence ( everything is very walkable in Florence).

In Rome, Armando al Pantheon on a side street near the Pantheon. Very small, recommend reservations. http://www.armandoalpantheon.it/home.php. Also enjoyed Casa Copelle as well, http://www.casacoppelle.it/.

Many of the restaurants in Venice and Rome in the main tourist areas have two menus/ servings..one for the locals and one for the tourists!!

Our local tour guide told us about this and took us to a few of his favourite places(usually out of the way down some side street) and ordered for us based on what we wanted.

Tt