A Convent as Accommodation? I did and I'm not religious.
While traveling through Italy, my art history professor booked us students into religious colleges and convents. Wether it was to save money or because she thought osmosis would occur and our knowledge of Venetian Religious Art would be enhanced, I am not sure.
However, as a non-religious person I really didn't mind staying in a space dedicated to Christianity. The rooms were clean and the breakfast conversation was as interesting as the breakfast itself. But there is Wi-Fi, serene areas to write, relax and take in the sounds of the connecting church and the location is ideal for any traveler looking to explore a part of Venice that many tourists don't see.
The view from your room won't disappoint either, and unlike hostels, for some reason I just felt like my stuff was safer with the prying eyes of Mother Mary, the crucifix adorned in every room and paintings of Don Orione looking over you.