If you have a car, a good option is to visit some of the nice small towns that surrounds the city, in this vilages one can see how the life in the rural area is, i visited some towns of the area on my way to San Leo.
We hiked up the hill to a city park that was built around an old castle with amazing views of the city. On the way up we passed this graveyard. The size of it is overwhelming.
It might not sound like something you would want to see but it actually was pretty amazing.
Monthevarchi Arezzo, Italia
We just started walking uphill behind the church and we landed in an amazing city park with an old castle overlooking the city. Outstanding views of Arezzo, very quiet, and worth the walk up there.