Brilla (the pasta maker) has a restuarant school in Parma and can tailor instruction to your level and interest. Might be worth a look http://www.academiabarilla.com/
Some of my favorites are:
il Coccorone in Montefalco - The food is well prepared with local ingredients and traditional style. The great thing about Montefalco is that it is area where the world renowned Sagrantino grape and wine is grown and made. So you will have great food & great wine. Close to Perugia and worth the trip for a lunch or dinner. Largo Tempestivi +39 0742 379535
il Profeta in Florence - Just off the Arno and one of many great places to have traditional Tuscan food and feel like you are eating with family. Via Borgognissanti, 93 R - 55-212265
Trattoria Omero - typical Tuscan food in the hills just outside of Florence just behind the Piazzale Michelangelo. Via Pian dei Giullari, Arcetri +39 055 220053
Trattoria Sostanza - Serving large "communal" meals in Florence since the mid 1800's.