If you want a place close to almost everything go for Eleonora's and Marco's place. 10-minute walk from the Vatican and Castel Sant'Angelo. Just when you leave the apartment you will feel like living "Eat, Pray, Love" :D Lovely streets full of life and small restaurants. Also, very close it's a fruit and vegetable market where you can buy local products.
Marco was a great host and gave us some local tips! Thank you so much!