Don't miss places for my italian vacation
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.