Virtually any outdoor cafe in Rome is a wonderful place to people-watch.  Sit at a cafe on Via Condotti near the Piazza de Spagna to watch the wealthy shop at Dior and Fendi.  Go to Piazza Navona to watch musicians, performance artists and tourists take in the sights and sounds.  If you want to get away from tourists, a trip into Trastevere will give you a slice of real Roman living.

Piazza Navona

Spanish Steps, looking at Via Condotti