-With no hesitation, you have to go straight to the Piazza del Campo. In fact, it shouldn't be too difficult, as most of the streets inside the walls lead to this square. This old field is known today for its beauty (its shell shape, the beautiful Palazzo Publico), but also for the horse race twice a year (the "Palio").
-Around the square, you will find several museums. Among them, the Museo Civico in the Palazzo Pubblico offers the advantage of giving acces to the Torre del Mangia from where you will have a wonderfull view on the square and the neighbourhood. But don't take it wrong. The masterpieces inside the museum definitely worth the entrance!