Hey, MaryM,
I'll be happy to share with you the regular "safe" places we dine, but please keep in mind, we are not dealing with milk, just pa/tna and eggs.
In Franklin near the McEwen Drive or Cool Spring Blvd exits there is a Moe's, a Chipotle and a Chick-fil-a. (There's also a Wendy's and a McDonald's in this location, but we don't eat there much.)
For sit down restaurants, there is a Cracker Barrel near the Murfreesboro Rd exit (across from the hospital), a Famous Dave's on Baker's Bridge Road near the Cool Springs Galleria, and an amazing Outback on Moore's Lane. All three of these have allergy menus that the managers will bring out to you if you ask.
I'm not sure where you may be visiting while in the Nashville area, but there is a Spaghetti Factory in downtown Nashville that has in the past been great (no egg in the pasta) and there is a Rainforest Cafe in Opry Mills that has always seemed very knowledgeable and accommodating.
If you have a lot of questions, feel free to pm me. I'll be happy to help!