Oh my dude. There are literally thousands of places to eat and things to see in the cities that you mentioned. The good news is, you can't go wrong and you can't make a mistake. You can't eat everywhere and see everything, but where you do choose to eat will be great and the things you see will be incredible.
Rather than bombard you with actual restaurant names, I'll just say this: avoid anything that looks like it caters to American tourists. Avoid any restaurant that has a tourist menu ("menu turistico"). Do these two things, and you can't go wrong. You can pick little hole-in-the-wall places that look like nothing outside, but once you go in you see that it is actually very quaint, and the food will be amazing. Rome, in particular, has thousands of these little places, as does Florence. Venice is a little bit different, but it's very similar.
I don't normally ask for advice in hotels, but my first time in Florence I was still a novice and we asked at the hotel front desk for a restaurant reservation. The guy told us where to go, which wasn't far away. Well, this place was shall we say very unimpressive from the outside. It was literally just a doorway with little signage, but we figured it must have been the place because there wasn't anything else around. Well. We went inside, fully expecting to turn around and leave, and it was amazing. The food was incredible, the wine list was extensive and extremely fairly priced, and the whole place was rocking. You'd have never guessed from the outside. I never forgot that lesson.
The other thing is, the places that the locals and the cognescenti go to don't open early for dinner. Some of them don't open until damned near 8pm, and the locals don't go for dinner there until 9. If you show up too early, they will know that you are a dumb tourist. And as a rule of thumb, if they are serving dinner at 6pm, you probably don't want to go there.
I remember being in Siena, dead tired on the first day of our arrival, and going into a restaurant at 930pm down off of the Campo. It was just getting started around then. When we left after 11 every table was full, and the place was glorious. In the smaller cities, like Siena in particular but even in Florence and Rome at a lot of places, the table is yours for the night. They don't assume that you will leave and some other party will sit at your table next. It's your table. At least, in the smaller non-touristy places, this is what you can expect.
You will love it all.