Branson is geared for tourists, so your best bet would be to ask some locals when you get there. I used to enjoy the Farmhouse and the Branson Cafe, both downtown. It's been years, though. There used to be a couple of BBQ places that were pretty good (Missouri style smoked with Hickory
), but I don't remember the names, so again, I'd ask around.
Something a little different is the Friendship House at the College of the Ozarks. The meals are prepared by the students.
Regardless, you can always go to the Steak n' Shake, which is a wonderful "road-chain" in itself.