A great place that is open all day long, You will find it in the large, open, Piazza Santa Cecila in Trastevere.
The sunshine streams in, there are comfy chairs, great coffee and pastries, terrific music playing and walls lined with beautiful photography and design books. What's not to like.
Whenever I am over on this side of the river I pay a visit to the shrine of the beautiful Santa Cecila, on the other side of the piazza. She is the patron saint of musicians.