Disagree with Trastevere. While it is certainly is less touristy, there are great restaurants all over Rome. Trastevere is a residential area. Not much to look at, especially in the evenings.
If in Rome only for a few days, why leave the areas you came to see. Yes, they are touristy but, you have a very short time to see the place. The touristy areas are spectacular and well lit during the evening. There are great restaurants and even street entertainers.
If I was in Rome (or Florence or Venice)for a week or more then I would agree to get off the beaten path for a bit of quiet but, in 3 days, you need to absorb what has made the place attractive enough for you to spend lots of money to see.
Is it solipsistic here? Or is it just me?