The historic center of Siena is not a large area. You should be fine on you own. With only a few hours available to see the city, I would recommend that you focus on the Duomo, the Duomo Museum and Santa Maria Della Scala followed by a visit to the Campo and the Civic Museum. Grab a seat at one of the restaurants in the Campo for an aperitivo.
As for dining, my personal favorites are La Torre (right beside the civic museum in the Campo area at Via Salicotto 7-9) for traditional Tuscan food - no menu, just the 4 or 5 dishes they have prepared that day. Or Osteria da Trombicche at Via Della Terme 66 (about 5 minutes from the Campo) for a more modern twist on traditional Italian food. In either case a reservation is recommended.
Hope you have a great visit to my favorite city in Italy.