So here is a link to one of my favorites thus far. It is big enough without being too big. It has beautiful views of trees (while that is a given here in the Santa Cruz Mountains it is not in Rome) and it is under my budget! It is not perfect, I am not crazy about the loads of blue tile, but it will give you an idea of what is available.
If you want there is a google map available on the bottom of the page. I am going to be living near Monte Mario, which is just a jaunt away from Vatican City.
(this is a picture from Brian and Sarah's roof top the radio tower is for the Vatican and the hill is Monte Mario)