I spent six months in Rome, mostly learning Italian but also using it as a base for being a tourist throughout Italy.
You are doing **enough already **on your Rome/Florence axis already, especially with side trips to Pisa and Venice. Italy will be hot and crowded where you are going, try to slow down and don’t sweat it. Forget adding extra destinations to your trip (although it is hard not to recommend staying in Lucca - we used it as a base for exploring Florence and Pisa as much cheaper and has a direct quick train line to both!) .
Pisa is fine, you are going whatever folk say so enjoy. The whole complex of the Cathedral, Baptistry, Campanile (Leaning Tower) and Camposanto is greater than the sum of it’s parts. It is full of folk selling tat and pick pockets (who are very good at their trade - be aware) but I’ve been twice and not regretted it.
I would strongly recommend **against **heading down to Pompeii this time - you will waste too much time getting down there and back. Force yourself to go back and do that then, together with Herculaneum, and stay on the Almalfi Coast. If you are into Greek ruins you can then also visit Paestum just to the south. Naples itself gets a bad rape and deserves a stay - and Capri too (which transends it tourist trap image if you can be bothered to walk more than a kilometer away from where the hordes stay mooing contentedly). That is another week all together.
Rome has been well covered by others above. All I would add is try to have a meal in Trastevere (literally “over the Tiber” - on the south bank) which is where many Romans still go for a really good meal. I know most Americans struggle with offal but this was where Rome’s butchers lived. They got the offal as part of their pay and so Roman cuisine is full of excellent offal recipes. If you like it then this is the place to go - if not go anyway it is full of all the mainstream options too. If you want to look like you know what you are doing drink beer with pizza and wine otherwise - the Italian (or at least Roman way).
Roman pizza are all crispy thin base and don’t come loaded with topping - don’t bother asking for deep pan or thicker varieties - and prepare for a different (better) experience where less is more.
Eat ice cream every day - Italians most often don’t bother with desert in the evening and have an ice cream whilst walking home. Never order it in a cafe (especially a popular one) served in cups etc - I’ve seen people get a bill larger than the lunch bill for doing so. Have a cone or a paper cup and walk and eat.
Drink coffee (espresso or a ***dopio ***(a double espresso)) at bars standing up. You should get a small glass of water with an ice cube in it for palate afterwards if the place is any good. Don’t expect a big breakfast - Italians generally get on with a coffee and a cornetto (a sort of Italian croissant). Don’t order cappuccino after 11 o’clock or latte in the afternoon or evenings.
Florence is great too - all the obvious sights are worth it, especially a walk down the river for a little while. As you like your food I would highly recommend getting your teeth into a real bistecca alla Fiorentina. It will be eye-wateringly expensive but worth every euro. It is a double steak with the T-bone retained from specially fed herds if it is a real one. Do some research for a good place first.
I could go on - you have realized your first mistake already which is trying to do too much with too short a stay. I would recommend enjoying getting your bearings on a few places over rushing around trying to see everything. Venice on a day-trip I would probably park, but I understand the draw. For me, I would not go unless I could wake up and look out of the window onto the lagoon or the Canal Grande.
Enjoy yourselves. We’re off to Lake Como for a wedding next weekend but then escaping to the lesser known Lago d’Orta for a holiday. A new area to me so looking forward to it myself.