I'm jealous. Love Rome. Below are some of our favorites from our last trip in November. As mentioned above, reservations are pretty much a must in Rome. I would make reservations in Florence, too. I recommend booking at least a week in advance, especially if you want the later dinner time (when all the locals eat). You'll need to call most restaurants. Also, from my experience, speaking a bit of italian when you walk in and being well dressed (not jeans, tshirt, and sneakers) will go a LONG way in receiving better service.
Rome:
La Tavernaccia - get the suckling pig
Colline Emiliane - perhaps our best meal
Trapizzino - great fast casual in trastevere
Roscioli - both the restaurant or bakery
Il Goccetto - great wine bar. Get there just before prime time, so you can grab a table. Recommend their appetizer special
[url=https://www.gelateriaromana.com/][/url]Gelateria La Romana - favorite gelato in Rome
Ebook for Rome restaurants. In addition to restaurant recommendations, it is helpful in understanding the dos and dont's at restaurants in Italy. Worth the few bucks.
https://katieparla.com/eating-and-drinking-in-rome-ebook/Florence:
I'Tuscani 2 - go if you like Florentine steak
la strega nocciola - best gelato in Florence