If you can get to the central part of Umbria, a great place to eat is the village of Monteflaco, home of the wold-renowned Sagrantino wine. Right off the main square in the village, is il Coccorone. One of the best meals we had in 2 weeks of traveling through Umbria. If you go there, don't miss the vine and if you have the time, many of the vineyards has tours and tastings. If you are a wine lover (or even liker) don't miss it.
Go to Naples for the best best pizza. Most of the pizza in Rome is for tourists. Eat the Carciofi alla giudia, Bucatini all'Amatriciana, Saltimboca alla Romana when in Rome. Going to Rome to eat pizza is like an Italian coming to the US, going to Maine for Fried Chicken.
I stayed in Umbria with my family for a week in 2005. We rented a Villa just outside of Spoleto. While I would not say that Spoleto is "full" of great restaurants, they certainly have several very good ones and are within a short drive of many other small villages that have great places to eat too. We had memorable meals in Montefalco (20KM), Spello (35KM), Deruta (48KM), Norcia (42KM) and Spoleto. These all worked out well with our touring schedule. We planned to be in certain places and researched the meals to coordinate with the travels.
In Genova: In the friggitoria department try: Antica Sciamada (vico San Giorgio,14) For a sit down place try: Antica Osteria della Foce (via ruspoli, 72, tel 0105533155) Or La Cantina di Colombo (via di porta soprano, 57, tel 0102475959 is a 35-seater with simple and delicious Trattoria del Liberale (via Monte Fasce, 91, tel 010395248) because it is all Genova, all the time; pure Ligurian tradizione
San Remo: Paolo e Barbara. (via Roma, 47, tel 0184531653)
I used to eat there when I lived in Florence in the 1990's. It was more sophisticated than the trattorie to which I was used to going. Upscale food and service and excellent (back then). I've seen similar reviews from people that have been there more recently.
Will you have a car? If you do, between Rome and Florence (with a small detour into Umbria) is Monteflaco. There you will find Il Ristorante Coccorone - Largo Tempestivi Montefalco Phone +39 0742 379 535. Great for lunch or dinner. I know you said you are not big wine drinkers, but Montefalco is the home of the Sagrantino grape and you'll find it on their wine list and used in their dishes too. If you are not driving, don't bother.