Lunch Between Florence and Assisi
You might try Cortona. It's fairly close to the Perugia highway that you'll take toward Assisi once you leave the A1 at the Sinalunga interchange (about 80 km south of Florence). I had dinner recently at Pane e Vino (http://www.pane-vino.it/), which has covered outdoor seating on a street above and overlooking the delightful commune. Coming in, just follow follow follow the signs for centro up around the city to the north gate (this is hard to describe with words; check google maps). There you'll find parking. Enter through the gate, and the restaurant is about a 5-minute walk.
Alternatively, you could drive into Castiglione del Lago on Lake Trasimeno, also close to the highway (about 10 km).. When last there (albeit several years ago), I had a very pleasant lunch at L'Aquario (http://www.ristorantelacquario.it/). Again, if you follow the signs for centro as far as you can, you'll end up at a parking area close to the main gate. The restaurant is just a few meters in. There are a number of other acceptable restaurants in this charming town as well.
Be sure to check for holiday closures. Also, a reservation is a good idea for L'Acquario, as it's a popular spot for locals for lunch.
Via Vittorio Emanuele II, 69, Castiglione del Lago, Umbria 06061, IT