Draft Book is a nice cozy little bar located right next to Campo de Fiori. Located right in the center of old Rome, Draft Book is a great place to start the night at. This small intimate spot has a nice collection of different books to check out while you have a drink. Art, Music, Cinema are some of the related topics. The even have book swap program, you bring one and you can tack one home.
Even if your not into books, the place has a chill ambiance and a vast selection of the finest abbeys of Belgian, France and other European countries. Draft also has a nice selection of Italian wine. They are known for making a mean mojito. Maybe try a super chilled shot of vodka.
I have been here several times and definitely recommend this spot. The people are very friendly and they also make really tasty food. Again, you are well located to go bar hoping right in walking distance.