I can't answer your question about where the locals eat in Savannah but there are some great restaurants down by the riverfront. We visited Savannah a couple of years ago and tried several of those establishments. Yum!
Trust me, it's not on River Street. Basically, all the restaurants on River Street are way overpriced and not really that good, as they are designed for tourists. There are better places a few streets up on Broughton St. and Congress St.
You certainly know Savannah. I totally agree with you about River Street. It is such a shame that a lot of people think that Savannah is defined by what they see and experience down there. When we were there I don't think we ate at one restaurant anywhere near the waterfront, but we had some incredible meals there.