Special restaurant in Rome

We will be traveling to Italy in July with our family of four and meeting some dear friends (a family of five) at the end of our trip in Rome. While we are in Rome, we will be celebrating our 20th anniversary and want to pick a special restaurant to celebrate with the nine of us. Special, to me, does not necessarily mean expensive. We want something warm, friendly, authentic and, most importantly, not touristy (though the latter may be hard to find in Rome in July.) Thanks in advance for any suggestions!