I got some ideasI've got some ideas for ya. Sorry I can't give directions though. You may have to call the places if you want to go there.
There is a place called BT Bones that's really good. There is a Shorty Smalls that's good too. I think that is a chain. Maybe a regional one? It's still real good. There are several good BBQ places. But... there are two that I can recommend that isn't necesarily BBQ but worth a stop.
One is called McFarland's. It's inside the mall that has Imax is the best way I can tell you how to find it. It's down home cooking stuff. I've never had anything bad there. Their chicken pot pie is awesome. My wife loves their meatloaf. BUT... even though the food is great, that's not why I'm recommending it. You can enjoy great food and have a bit of prank at the same time. I don't know how many people you will have with you but they have a round table that will seat about six. You can request this table on the down low so only you know about it. The prank is that the table slowly... and I mean slowly rises. It rises so slowly that you never notice that it's moving. You just go for a bite and "all of a sudden" the table is chest high. It may seem corny. Maybe it is. I don't know, but I did it with my family and they all got a huge kick out of it.
Okay... the other one is not actually in Branson. It's between Branson and Springfield on hwy 65 in Ozark, MO. It's called Lambert's. There is almost always about an hour wait to get in that place but it's worth it. You can get all you can eat ribs! That's right. All you can it. And they are good ribs too! Plus it's a fun place too because they throw rolls all around the room. They way it works, is everything is all you can eat. What ever entree you order, which they have a lot to choose from. Ribs is just one choice. There is also steak, pork chops, I can't remember what all but good stuff. They bring side dishes around "family style". It's a great place.
Have fun. Hope this helped.